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Wyszukujesz frazę "operator measures" wg kryterium: Temat


Wyświetlanie 1-6 z 6
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:
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:
Vector and operator valued measures as controls for infinite dimensional systems: optimal control
Autorzy:
Ahmed, N.
Powiązania:
https://bibliotekanauki.pl/articles/729468.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
evolution equations
Banach spaces
operator valued measures
strong operator topology
existence of solutions
optimal control
Opis:
In this paper we consider a general class of systems determined by operator valued measures which are assumed to be countably additive in the strong operator topology. This replaces our previous assumption of countable additivity in the uniform operator topology by the weaker assumption. Under the relaxed assumption plus an additional assumption requiring the existence of a dominating measure, we prove some results on existence of solutions and their regularity properties both for linear and semilinear systems. Also presented are results on continuous dependence of solutions on operator and vector valued measures, and other parameters determining the system which are then used to prove some results on control theory including existence and necessary conditions of optimality. Here the operator valued measures are treated as structural controls. The paper is concluded with some examples from classical and quantum mechanics and a remark on future direction.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2008, 28, 1; 95-131
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control of systems determined by strongly nonlinear operator valued measures
Autorzy:
Ahmed, N.
Powiązania:
https://bibliotekanauki.pl/articles/729396.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
evolution equations
strongly nonlinear operator valued measures
existence of solutions
regularity properties
optimal control
Opis:
In this paper we consider a class of distributed parameter systems (partial differential equations) determined by strongly nonlinear operator valued measures in the setting of the Gelfand triple V ↪ H ↪ V* with continuous and dense embeddings where H is a separable Hilbert space and V is a reflexive Banach space with dual V*. The system is given by
dx + A(dt,x) = f(t,x)γ(dt) + B(t)u(dt), x(0) = ξ, t ∈ I ≡ [0,T]
where A is a strongly nonlinear operator valued measure mapping Σ × V to V* with Σ denoting the sigma algebra of subsets of the set I and f is a nonlinear operator mapping I × H to H, γ is a countably additive bounded positive measure and the control u is a suitable vector measure. We present existence, uniqueness and regularity properties of weak solutions and then prove the existence of optimal controls (vector valued measures) for a class of control problems.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2008, 28, 1; 165-189
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Weak compactness in the space of operator valued measures $M_ba(Σ,(X,Y))$ and its applications
Autorzy:
Ahmed, N.
Powiązania:
https://bibliotekanauki.pl/articles/729361.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
space of operator valued measures
weak compactness
semigroups of bounded linear operators
optimal structural control
Opis:
In this note we present necessary and sufficient conditions characterizing conditionally weakly compact sets in the space of (bounded linear) operator valued measures $M_{ba}(Σ,(X,Y))$. This generalizes a recent result of the author characterizing conditionally weakly compact subsets of the space of nuclear operator valued measures $M_{ba}(Σ,₁(X,Y))$. This result has interesting applications in optimization and control theory as illustrated by several examples.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2011, 31, 2; 231-247
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Topological dual of $B_∞(I, ₁(X,Y))$ with application to stochastic systems on Hilbert space
Autorzy:
Ahmed, N.
Powiązania:
https://bibliotekanauki.pl/articles/729390.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
representation theory
topological dual
finitely additive operator-valued measures
polish space
Hilbert space
stochastic systems
structural control
uncertainty abatement
Opis:
In this paper, we prove that the topological dual of the Banach space of bounded measurable functions with values in the space of nuclear operators, furnished with the natural topology, is isometrically isomorphic to the space of finitely additive linear operator-valued measures having bounded variation in a Banach space containing the space of bounded linear operators. This is then applied to a stochastic structural control problem. An optimal operator-valued measure, considered as the structural control, is to be chosen so as to minimize fluctuation (volatility). Both existence of optimal policy and necessary conditions of optimality are presented including a conceptual algorithm.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2009, 29, 1; 67-90
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
    Wyświetlanie 1-6 z 6

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