Topological properties of some spaces of continuous operators

Marian Nowak

ArticleOriginal scientific text

Title

Topological properties of some spaces of continuous operators

Authors ¹

Affiliations

Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, ul. Szafrana 4A, 65-516 Zielona Góra, Poland

Abstract

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, {| | \cdot | |}_{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.

Keywords

ENG

spaces of vector-valued continuous functions, strict topologies, operator measures, topology of simple convergence, continuous operators

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Title

Topological properties of some spaces of continuous operators

Affiliations

Abstract

Keywords

Bibliography