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    Wyświetlanie 1-21 z 21
    Tytuł:
    On type-2 m-topological spaces
    Autorzy:
    Nazmul, Sk.
    Powiązania:
    https://bibliotekanauki.pl/articles/744630.pdf
    Data publikacji:
    2017-12-01
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    Multi sets
    multi topologies
    multi subspace
    m2-topologies
    mgp-maps
    Opis:
    In the present paper, we define a notion of an m2-topological space by introducing a count of openness of a multiset (mset in short) and study the properties of m2-subspaces, mgp-maps etc. Decomposition theorems involving m-topologies and m2-topologies are established. The behaviour of the functional image and functional preimage of an m2-topologies, the continuity of the identity mapping and a constant mapping in m2-topologies are also examined.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica; 2017, 16
    2300-133X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Duality and some topological properties of vector-valued function spaces
    Autorzy:
    Feledziak, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/746589.pdf
    Data publikacji:
    2008
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    vector-valued function spaces
    locally solid topologies
    KB-spaces
    Levy topologies
    Lebesgue topologies
    order dual
    order continuous dual
    perfectness
    Opis:
    Let \(E\) be an ideal of \(L^0\) over \(\sigma\)-finite measure space \((\Omega, \Sigma, \mu)\) and let \((X, \| \cdot \|_X)\) be a real Banach space. Let \(E(X)\) be a subspace of the space \(L^0(X)\) of \(\mu\)-equivalence classes of all strongly \(\Sigma\)-measurable functions \(f\colon \Omega \to X\) and consisting of all those \(f\in L^0(X)\), for which the scalar function \(\tilde{f} = \|f (\cdot)\|_X\) belongs to \(E\). Let \(E\) be equipped with a Hausdorff locally convex-solid topology \(\xi\) and let \(\xi\) stand for the topology on \(E(X)\) associated with \(\xi\). We examine the relationship between the properties of the space \((E(X), \xi)\) and the properties of both the spaces \((E, \xi)\) and \((X, \|· \|_X)\). In particular, it is proved that \(E(X)\) (embedded in a natural way) is an order closed ideal of its bidual iff \(E\) is an order closed ideal of its bidual and \(X\) is reflexive. As an application, we obtain that \(E(X)\) is perfect iff \(E\) is perfect and \(X\) is reflexive.
    Źródło:
    Commentationes Mathematicae; 2008, 48, 1
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Cardinalities of lattices of topologies of unars and some related topics
    Autorzy:
    Kartashova, Anna
    Powiązania:
    https://bibliotekanauki.pl/articles/728762.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    unar
    lattice of topologies
    lattice of congruences
    Opis:
    In this paper we find cardinalities of lattices of topologies of uncountable unars and show that the lattice of topologies of a unar cannor be countably infinite. It is proved that under some finiteness conditions the lattice of topologies of a unar is finite. Furthermore, the relations between the lattice of topologies of an arbitrary unar and its congruence lattice are established.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 2; 129-137
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the comparison of the density type topologies generated by sequences and by functions
    Autorzy:
    Filipczak, Małgorzata
    Filipczak, Tomasz
    Powiązania:
    https://bibliotekanauki.pl/articles/746528.pdf
    Data publikacji:
    2009
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    density points
    density topology
    comparison of topologies
    Opis:
    In the paper we investigate density type topologies generated by functions \(f\) satisfying condition \(\liminf_{x \gt 0^+} \frac{f(x)}{x}\), which are not generated by any sequence.
    Źródło:
    Commentationes Mathematicae; 2009, 49, 2
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Adherence of minimizers for dual convergences
    Autorzy:
    Dolecki, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/970255.pdf
    Data publikacji:
    2007
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    stability of minimizers
    continuous convergence
    dual topologies
    Opis:
    It is proved that many known convergences (e.g., continuous convergence, Isbell topology, compact-open topology, point-wise convergence) on the space of continuous maps (valued in a topological space) can be represented as the dual convergences with respect to collections of families of sets, and that they can be characterized in terms of the corresponding hyperspace convergences of the inverse images of closed sets. As a result, the convergence of real-valued functions for a dual convergence implies the convergence of their sets of minima on the corresponding hyperspace.
    Źródło:
    Control and Cybernetics; 2007, 36, 3; 647-658
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Bochner representable operators on Köthe-Bochner spaces
    Autorzy:
    Nowak, Marian
    Powiązania:
    https://bibliotekanauki.pl/articles/745751.pdf
    Data publikacji:
    2008
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Köthe-Bochner spaces
    Generalized DF-spaces
    Bochner representable operators
    Weakly compact operators
    Compact operators
    Mixed topologies
    Mackey topologies
    Opis:
    Let \(E\) be a Banach function space and \(X\) be a real Banach space. We study Bochner representable operators from a Köthe-Bochner space \(E(X)\) to a Banach space \(Y\). We consider the problem of compactness and weak compactness of Bochner representable operators from \(E(X)\) (provided with the natural mixed topology) to \(Y\).
    Źródło:
    Commentationes Mathematicae; 2008, 48, 2
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Uniformly \(\mu\)-Continuous Topologies on Orlicz-Bochner Spaces
    Autorzy:
    Feledziak, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/746216.pdf
    Data publikacji:
    2006
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Orlicz spaces
    Orlicz-Bochner spaces
    locally solid topologies
    generalized mixed topologies
    uniformly \(\varphi\)-summable sets
    uniformly \(\varphi\)-integrable sets
    Opis:
    We examine the topological properties of Orlicz-Bochner spaces \(L^\varphi(X)\) (over a σ-finite measure space \((\Omega, \Sigma, \mu))\), where \(\varphi\) is an Orlicz function (not necessarily convex) and \(X\) is a real Banach space. We continue the study of some class of locally convex topologies on \(L^\varphi (X)\), called uniformly \(\mu\)-continuous topologies. In particular, the generalized mixed topology \(\mathcal{T}_I^\varphi (X)\) on \(L^\varphi (X)\) (in the sense of Turpin) is considered.
    Źródło:
    Commentationes Mathematicae; 2006, 46, 1
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A new approach to detecting and preventing populations stagnation through dynamic changes in multi-population-based algorithms
    Autorzy:
    Łapa, Krystian
    Rutkowska, Danuta
    Byrski, Aleksander
    Napoli, Christian
    Powiązania:
    https://bibliotekanauki.pl/articles/23944836.pdf
    Data publikacji:
    2023
    Wydawca:
    Społeczna Akademia Nauk w Łodzi. Polskie Towarzystwo Sieci Neuronowych
    Tematy:
    multi-population-based algorithms
    migration topologies
    population stagnation
    Opis:
    In this paper, a new mechanism for detecting population stagnation based on the analysis of the local improvement of the evaluation function and the infinite impulse response filter is proposed. The purpose of this mechanism is to improve the population stagnation detection capability for various optimization scenarios, and thus to improve multi-population-based algorithms (MPBAs) performance. In addition, various other approaches have been proposed to eliminate stagnation, including approaches aimed at both improving performance and reducing the complexity of the algorithms. The developed methods were tested, among the others, for various migration topologies and various MPBAs, including the MNIA algorithm, which allows the use of many different base algorithms and thus eliminates the need to select the population-based algorithm for a given simulation problem. The simulations were performed for typical benchmark functions and control problems. The obtained results confirm the validity of the developed method.
    Źródło:
    Journal of Artificial Intelligence and Soft Computing Research; 2023, 13, 4; 289--306
    2083-2567
    2449-6499
    Pojawia się w:
    Journal of Artificial Intelligence and Soft Computing Research
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Topology optimization of trusses using bars exchange method
    Autorzy:
    Bojczuk, D.
    Rębosz-Kurdek, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/202330.pdf
    Data publikacji:
    2012
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    trusses
    algorithm of optimization
    optimal topologies
    bars exchange
    Opis:
    The algorithm of optimization of trusses is presented in the paper, where for topology optimization the bars exchange method is used. In the first case, the problem aimed at cost minimization with a constraint set on global stiffness is formulated. In the second case, the problem of minimizing the cost function subjected to stress and cross-sectional area constraints is discussed and here the multiple-load case is taken into consideration. The conditions for introduction of topology modification and its acceptance are specified. The paper is illustrated with three examples.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2012, 60, 2; 185-189
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The symmetric tensor product of a direct sum of locally convex spaces
    Autorzy:
    M Ansemil, José
    Floret, Klaus
    Powiązania:
    https://bibliotekanauki.pl/articles/1218462.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    symmetric tensor products
    continuous n-homogeneous polynomials
    tensor topologies
    Opis:
    An explicit representation of the n-fold symmetric tensor product (equipped with a natural topology τ such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for $⨂^n_{τ,s} (F_1⨁ F_2)$ gives a direct proof of a recent result of Díaz and Dineen (and generalizes it to other topologies τ) that the n-fold projective symmetric and the n-fold projective "full" tensor product of a locally convex space E are isomorphic if E is isomorphic to its square $E^2$.
    Źródło:
    Studia Mathematica; 1998, 129, 3; 285-295
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The effect of winding topologies on the performance of flux-switching permanent magnet machine having different number of rotor poles
    Autorzy:
    Chijioke Awah, Ch.
    Inya Okoro, O.
    Powiązania:
    https://bibliotekanauki.pl/articles/140434.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    average torque
    copper loss
    phase back-EMF
    winding topologies
    Opis:
    Comparison of the electromagnetic performance of a flux-switching permanent magnet (PM) machine having two separate stators as well as different winding topologies is investigated in this paper. Different stator and rotor pole combinations of these machines are also considered. The analysis includes the open-circuit and on-load characteristics of the analyzed machines. It is observed that, the largest fundamental values of electromagnetic torque, for each winding topology, is seen in the 11-rotor-pole and 10-rotor-pole machines having alternate- and all-pole-wound configurations, respectively. Moreover, significant ripple is observed in the waveforms of the even-number rotor pole machines compared to their corresponding odd-number rotor pole counterparts. Overall, the alternate-pole-wound machines essentially have larger torque-density than their equivalent all-pole-wound ones. The investigated machine is also tested for validation.
    Źródło:
    Archives of Electrical Engineering; 2018, 67, 4; 845-855
    1427-4221
    2300-2506
    Pojawia się w:
    Archives of Electrical Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Topologies and bornologies determined by operator ideals, II
    Autorzy:
    Wong, Ngai-Ching
    Powiązania:
    https://bibliotekanauki.pl/articles/1290169.pdf
    Data publikacji:
    1994
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    operator ideals
    locally convex spaces
    topologies
    bornologies
    Grothendieck spaces
    Opis:
    Let be an operator ideal on LCS's. A continuous seminorm p of a LCS X is said to be - continuous if $Q̃_p ∈ ^{inj}(X,X̃_p)$, where $X̃_p$ is the completion of the normed space $X_p = X/p^{-1}(0)$ and $Q̃_p$ is the canonical map. p is said to be a Groth()- seminorm if there is a continuous seminorm q of X such that p ≤ q and the canonical map $Q̃_{pq} : X̃_q → X̃_p$ belongs to $(X̃_q,X̃_p)$. It is well known that when is the ideal of absolutely summing (resp. precompact, weakly compact) operators, a LCS X is a nuclear (resp. Schwartz, infra-Schwartz) space if and only if every continuous seminorm p of X is -continuous if and only if every continuous seminorm p of X is a Groth()-seminorm. In this paper, we extend this equivalence to arbitrary operator ideals and discuss several aspects of these constructions which were initiated by A. Grothendieck and D. Randtke, respectively. A bornological version of the theory is also obtained.
    Źródło:
    Studia Mathematica; 1994, 111, 2; 153-162
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Compactness and countable compactness in weak topologies
    Autorzy:
    Kirk, W. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/1289854.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    weak topologies
    compactness
    countable compactness
    quasi-normal structure
    convexity structures
    Opis:
    A bounded closed convex set K in a Banach space X is said to have quasi-normal structure if each bounded closed convex subset H of K for which diam(H) > 0 contains a point u for which ∥u-x∥ < diam(H) for each x ∈ H. It is shown that if the convex sets on the unit sphere in X satisfy this condition (which is much weaker than the assumption that convex sets on the unit sphere are separable), then relative to various weak topologies, the unit ball in X is compact whenever it is countably compact.
    Źródło:
    Studia Mathematica; 1994-1995, 112, 3; 243-250
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Comparison of ψ -sparse topologies
    Autorzy:
    Goździewicz-Smejda, A.
    Łazarow, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/121849.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
    Tematy:
    funkcje matematyczne
    topologie gęstości
    zbiory mierzalne
    mathematical function
    density topologies
    continuous functions
    Opis:
    The paper includes a necessary condition and sufficient conditions under which two ψ -sparse topologies generated by two functions ψ1 and ψ 2 are equal. Additionally we proved that the intersection of all ψ -sparse topologies is equal to the Hashimoto topology.
    Źródło:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2009, 14; 21-36
    2450-9302
    Pojawia się w:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Topological properties of the complex vector lattice of bounded finitely additive mesures
    Autorzy:
    Nowak, Marian
    Powiązania:
    https://bibliotekanauki.pl/articles/1912867.pdf
    Data publikacji:
    2013
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    complex vector lattices
    locally solid topologies
    spaces of bounded finitely additive measures
    Opis:
    Let \(\Sigma\) be a \(\sigma\)-algebra of subsets of a non-empty set \(\Omega\). Let \(ba(\Sigma)\) be the complex vector lattice of bounded finitely additive measures \(\mu:\Sigma\rightarrow\mathbb{C}\). We study locally solid topologies on \(ba(\Sigma)\). We develop the duality theory of \(ba(\Sigma)\), provided with locally convex-solid topologies.
    Źródło:
    Commentationes Mathematicae; 2013, 53, 2; 371-382
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dimming control schemes combining IEEE 802.15.7 and SC-LPPM modulation schemes with an adaptive M-QAM OFDM for indoor LOS VLC systems
    Autorzy:
    Mohammed, Nazmi A.
    Badawi, Kareem A.
    Khalaf, Ashraf A. M.
    El-Rabaie, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/1818236.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Stowarzyszenie Elektryków Polskich
    Tematy:
    visible light communication
    sub-carrier pulse position modulation
    lightning topologies
    bit error rate
    Opis:
    The presented work proposes a new dimming control schemes for indoor visible light communication which combines variable pulse-position modulation, colour shift keying as key schemes of IEEE 802.15.7 standard, and sub carrier-pulse-position modulation as a pulse-position modulation variant with orthogonal frequency division multiplexing. These schemes are then compared with traditional merging schemes utilizing pulse-width modulation and multiple pulse-position modulation with m-ary quadrature amplitude modulation OFDM. The proposed schemes are investigated in a typical room with a different lighting layout (i.e., distinctive and uniform lighting layout), followed by an illumination investigation to evaluate the performance of the proposed schemes, especially the enhanced achieved data rates, and to determine their limitations as reliable visible light communication systems that can satisfy both communication and illumination requirements.
    Źródło:
    Opto-Electronics Review; 2020, 28, 4; 203--212
    1230-3402
    Pojawia się w:
    Opto-Electronics Review
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dimming control schemes combining IEEE 802.15.7 and SC-LPPM modulation schemes with an adaptive M-QAM OFDM for indoor LOS VLC systems
    Autorzy:
    Mohammed, Nazmi A.
    Badawi, Kareem A.
    Khalaf, Ashraf A. M.
    El-Rabaie, El-Sayed
    Powiązania:
    https://bibliotekanauki.pl/articles/1818230.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Stowarzyszenie Elektryków Polskich
    Tematy:
    visible light communication
    sub-carrier pulse position modulation
    lightning topologies
    bit error rate
    Opis:
    The presented work proposes a new dimming control schemes for indoor visible light communication which combines variable pulse-position modulation, colour shift keying as key schemes of IEEE 802.15.7 standard, and sub carrier-pulse-position modulation as a pulse-position modulation variant with orthogonal frequency division multiplexing. These schemes are then compared with traditional merging schemes utilizing pulse-width modulation and multiple pulse-position modulation with m-ary quadrature amplitude modulation OFDM. The proposed schemes are investigated in a typical room with a different lighting layout (i.e., distinctive and uniform lighting layout), followed by an illumination investigation to evaluate the performance of the proposed schemes, especially the enhanced achieved data rates, and to determine their limitations as reliable visible light communication systems that can satisfy both communication and illumination requirements.
    Źródło:
    Opto-Electronics Review; 2020, 28, 4; 203--212
    1230-3402
    Pojawia się w:
    Opto-Electronics Review
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Coincidence of topologies on tensor products of Köthe echelon spaces
    Autorzy:
    Bonet, J.
    Defant, A.
    Peris, A.
    Ramanujan, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/1290127.pdf
    Data publikacji:
    1994
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Köthe echelon spaces
    topological tensor products
    injective and projective topologies
    tensor products of diagonal operators
    Opis:
    We investigate conditions under which the projective and the injective topologies coincide on the tensor product of two Köthe echelon or coechelon spaces. A major tool in the proof is the characterization of the επ-continuity of the tensor product of two diagonal operators from $l_p$ to $l_q$. Several sharp forms of this result are also included.
    Źródło:
    Studia Mathematica; 1994, 111, 3; 263-281
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Topological properties of some spaces of continuous operators
    Autorzy:
    Nowak, Marian
    Powiązania:
    https://bibliotekanauki.pl/articles/729596.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    spaces of vector-valued continuous functions
    strict topologies
    operator measures
    topology of simple convergence
    continuous operators
    Opis:
    Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let $C_b(X,E)$ be the space of all E-valued bounded continuous functions on X, equipped with the strict topology β. We study topological properties of the space $L_{β}(C_{b}(X,E),F)$ of all $(β,||·||_{F})$-continuous linear operators from $C_{b}(X,E)$ to F, equipped with the topology $τ_{s}$ of simple convergence. If X is a locally compact paracompact space (resp. a P-space), we characterize $τ_{s}$-compact subsets of $L_{β}(C_{b}(X,E),F)$ in terms of properties of the corresponding sets of the representing operator-valued Borel measures. It is shown that the space $(L_{β}(C_{b}(X,E),F),τ_{s})$ is sequentially complete if X is a locally compact paracompact space.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2016, 36, 1; 79-86
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Weakly precompact operators on $C_{b}(X,E)$ with the strict topology
    Autorzy:
    Stochmal, Juliusz
    Powiązania:
    https://bibliotekanauki.pl/articles/729586.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    spaces of vector-valued continuous functions
    strict topologies
    operator measures
    strongly bounded operators
    weakly precompact operators
    Opis:
    Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let $C_{b}(X,E)$ be the space of all E-valued bounded continuous functions on X, equipped with the strict topology β. We study weakly precompact operators $T:C_{b}(X,E) → F$. In particular, we show that if X is a paracompact k-space and E contains no isomorphic copy of l¹, then every strongly bounded operator $T:C_{b}(X,E) → F$ is weakly precompact.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2016, 36, 1; 65-77
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Compact Sets of Compact Operators on Banach Spaces not Containing a Copy of \( l^1 \)
    Autorzy:
    Akkouchi, Mohamed
    Powiązania:
    https://bibliotekanauki.pl/articles/44447197.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    Compact sets of compact operators
    precompact sets
    Arzela-Ascoli Theorem
    relatively compact sets in Banach spaces
    duality
    weak topologies
    Banach spaces not containing a copy of l^1
    Opis:
    F. Galaz-Fontes (Proc. AMS., 1998) has established a criterion for a subset of the space of compact linear operators from a reflexive and separable space X into a Banach space Y to be compact. F. Mayoral (Proc. AMS., 2000) has extended this criterion to the case of Banach spaces not containing a copy of \( l^1 \). The purpose of this note is to give a new proof of the result of F. Mayoral. In our proof, we use \( l^\infty \)-spaces, a well known result of H. P. Rosenthal and L.E. Dor which characterizes the spaces without a copy of \( l^1 \) and a recent result obtained by G. Nagy in 2007 concerining compact sets in normed spaces. We point out that another proof of Mayoral’s result was given by E. Serrano, C. Pineiro and J.M. Delgado (Proc. AMS., 2006) by using a different method.
    Źródło:
    Acta Universitatis Lodziensis. Folia Mathematica; 2010, 17; 11-16
    2450-7652
    Pojawia się w:
    Acta Universitatis Lodziensis. Folia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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