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Topological properties of some spaces of continuous operators

100%

Nowak M.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2016

tom 36

nr 1

79-86

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.

Weakly precompact operators on $C_{b}(X,E)$ with the strict topology

100%

Stochmal J.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2016

tom 36

nr 1

65-77

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.

Ograniczanie wyników

2 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Nowak M.

1 Stochmal J.

2 2016

Wyniki wyszukiwania

Topological properties of some spaces of continuous operators

Weakly precompact operators on $C_{b}(X,E)$ with the strict topology