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    Wyświetlanie 1-5 z 5
    Tytuł:
    Generalized limits and a mean ergodic theorem
    Autorzy:
    Li, Yuan-Chuan
    Shaw, Sen-Yen
    Powiązania:
    https://bibliotekanauki.pl/articles/1220908.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Banach limits
    $L$-limits
    states
    numerical radius
    reflexive space
    mean ergodic theorem
    Opis:
    For a given linear operator L on $ℓ^∞$ with ∥L∥ = 1 and L(1) = 1, a notion of limit, called the L-limit, is defined for bounded sequences in a normed linear space X. In the case where L is the left shift operator on $ℓ^∞$ and $X = ℓ^∞$, the definition of L-limit reduces to Lorentz's definition of σ-limit, which is described by means of Banach limits on $ℓ^∞$. We discuss some properties of L-limits, characterize reflexive spaces in terms of existence of L-limits of bounded sequences, and formulate a version of the abstract mean ergodic theorem in terms of L-limits. A theorem of Sinclair on the form of linear functionals on a unital normed algebra in terms of states is also generalized.
    Źródło:
    Studia Mathematica; 1996, 121, 3; 207-219
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Weak uniform normal structure and iterative fixed points of nonexpansive mappings
    Autorzy:
    Domínguez Benavides, T.
    López Acedo, G.
    Xu, Hong
    Powiązania:
    https://bibliotekanauki.pl/articles/967052.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    nonexpansive mapping
    iterative fixed point
    geometrical coefficients of Banach spaces
    James' quasi-reflexive space
    weak uniform normal structure
    Opis:
    This paper is concerned with weak uniform normal structure and iterative fixed points of nonexpansive mappings. Precisely, in Section 1, we show that the geometrical coefficient β(X) for a Banach space X recently introduced by Jimenez-Melado [8] is exactly the weakly convergent sequence coefficient WCS(X) introduced by Bynum [1] in 1980. We then show in Section 2 that all kinds of James' quasi-reflexive spaces have weak uniform normal structure. Finally, in Section 3, we show that in a space X with weak uniform normal structure, every nonexpansive self-mapping defined on a weakly sequentially compact convex subset of X admits an iterative fixed point.
    Źródło:
    Colloquium Mathematicum; 1995, 68, 1; 17-23
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On a vector-valued local ergodic theorem in $L_∞$
    Autorzy:
    Sato, Ryotaro
    Powiązania:
    https://bibliotekanauki.pl/articles/1217311.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    vector-valued local ergodic theorem
    reflexive Banach space
    d-dimensional semigroup of linear contractions
    contraction majorant
    Opis:
    Let $T = {T(u): u ∈ ℝ_d^{+}}$ be a strongly continuous d-dimensional semigroup of linear contractions on $L_1((Ω,Σ,μ);X)$, where (Ω,Σ,μ) is a σ-finite measure space and X is a reflexive Banach space. Since $L_1((Ω,Σ,μ);X)* = L_∞((Ω,Σ,μ);X*)$, the adjoint semigroup $T* = {T*(u): u ∈ ℝ_d^{+}}$ becomes a weak*-continuous semigroup of linear contractions acting on $L_∞((Ω,Σ,μ);X*)$. In this paper the local ergodic theorem is studied for the adjoint semigroup T*. Assuming that each T(u), $u ∈ ℝ_d^{+}$, has a contraction majorant P(u) defined on $L_1((Ω,Σ,μ);ℝ)$, that is, P(u) is a positive linear contraction on $L_1((Ω,Σ,μ);ℝ)$ such that $‖T(u)f(ω)‖ ≤ P(u)‖f(·)‖(ω)$ almost everywhere on Ω for every $⨍ ∈ L_1((Ω,Σ,μ);X)$, we prove that the local ergodic theorem holds for T*.
    Źródło:
    Studia Mathematica; 1999, 132, 3; 285-298
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Rotundity and smoothness of convex bodies in reflexive and nonreflexive spaces
    Autorzy:
    Klee, Victor
    Veselý, Libor
    Zanco, Clemente
    Powiązania:
    https://bibliotekanauki.pl/articles/1287312.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    normed linear space
    reflexive
    convex body
    smooth
    rotund
    strictly convex
    vector sum
    convex hull
    stability
    Opis:
    For combining two convex bodies C and D to produce a third body, two of the most important ways are the operation ∓ of forming the closure of the vector sum C+D and the operation γ̅ of forming the closure of the convex hull of C ⋃ D. When the containing normed linear space X is reflexive, it follows from weak compactness that the vector sum and the convex hull are already closed, and from this it follows that the class of all rotund bodies in X is stable with respect to the operation ∓ and the class of all smooth bodies in X is stable with respect to both ∓ and γ̅. In our paper it is shown that when X is separable, these stability properties of rotundity (resp. smoothness) are actually equivalent to the reflexivity of X. The characterizations remain valid for each nonseparable X that contains a rotund (resp. smooth) body.
    Źródło:
    Studia Mathematica; 1996, 120, 3; 191-204
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Semantic Shifts and Stylistic Overtones as Conveyed by Function Verb Phrases. Comparative View: English, German, Rom
    Autorzy:
    MÁCIUCÁ, GINA
    Powiązania:
    https://bibliotekanauki.pl/articles/953875.pdf
    Data publikacji:
    2008-12-31
    Wydawca:
    Uniwersytet Opolski
    Tematy:
    function verb phrase
    marginal verb
    Aktionsart
    ingressive
    egressive
    stylistic synonymy
    implicit/explicit passive/reflexive
    time/space-saving function
    minor performer
    decomposition of idiomatic meaning
    linguicomedy
    translatability
    Opis:
    After painstakingly anatomizing in a previous book (s. DIP) the function verb phrase (FVP) in German and tracking down English combinations which display the morpho syntactical pattern, comply with the lexicosemantic criteria and assume the stylistic features, characteristic of “Funktionsverbgeflige” (FVGs), I resume in the present contribution my relentless quest for lexicomorphological conveyors of FVGs, this time in Romaniana Romance language - and then, in a second stage, try to go with a fine tooth-comb through the semantic and stylistic shifts following in the wake of FVPs as employed by the three languages at issue (German, English and Romanian). The opening section of the paper at hand searches in a first phase through the samples of Romanian FVPs extracted from various sources and assigns them to the aspect subcategories which they most fittingly illustrate: ingressive, punctual, iterative and egressive. In a second phase the analysis focuses on type a-§i ie$i din rábdári FVPs which convey a transition from one state to another and, consequently, admit of a double-barrelled interpretation, i.e. both egressive and ingressive - hence the labels ‘contradiction in terms’ and ‘transitive aspect’ I put forward as indicative of their idiosyncratic behaviour. The third and final phase of my survey is devoted to investigating stylistic synonymy as well as defending such intriguing FVPs as fa ll in love and fa ll out o f love. The approach in the middle section is roughly the same, i.e. descriptive in the beginning, with copious illustration of various semantic shifts (active / reflexive > passive, active > reflexive) as well as of the contrasts and similarities observed when comparing the three languages at issue, and interpretive in the second stage, with the focus on two most challenging cases: the ‘implicit’ passive with a subject acting semantically as a ‘minor performer’; the surprisingly divergent semantics of two at first blush similar FVPs {be thrown into ecstasies and go into ecstasies). The third section investigates the involuntary as well as premeditated decomposition of idiomatic meaning in FVPs, which more often than not is to be held accountable for comic effects. The technique at work here is the superimposition of nonidiomatic meaning on the idiomatic one, which in turn triggers off the reaction phase of the listener/reader confronted when least expected with the real intentions of the speaker/writer. The effects of the interference at issue range from ambiguity through a smack of ridicule - when decomposition is unintentional - to the most sophisticated linguistic humour - when decomposition is premeditated. Since the approach is also a contrastive one, the final conclusions would only naturally relate to the rendering into another language of linguicomedy samples. Unfortunately the translatability of interference-effects-generated linguistic humour has been found to be minimum at best in most cases.
    Źródło:
    Stylistyka; 2008, 17; 313-326
    1230-2287
    2545-1669
    Pojawia się w:
    Stylistyka
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-5 z 5

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