Extension of operators on spaces of vector-valued continuous functions

Let X be a completely regular Hausdorff space and let Ba stand for the Baire σ-algebra of sets in X. For a Banach space E let Crc(X,E) be the space of all continuous functions f:X→E such that f(X) is a relatively compact set in E, and let B(Ba,E) be the space of all totally Ba-measurable functions f...

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Bibliographic Details
Published in:Indagationes mathematicae Vol. 27; no. 1; pp. 20 - 28
Main Author: Nowak, Marian
Format: Journal Article
Language:English
Published: Elsevier B.V 01.01.2016
Subjects:
Integration operators
Spaces of vector-valued continuous functions
Strict topologies
Vector measures
Strict topologies
Vector measures
Spaces of vector-valued continuous functions
Integration operators
ISSN:0019-3577, 1872-6100
Online Access:Get full text
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Summary:Let X be a completely regular Hausdorff space and let Ba stand for the Baire σ-algebra of sets in X. For a Banach space E let Crc(X,E) be the space of all continuous functions f:X→E such that f(X) is a relatively compact set in E, and let B(Ba,E) be the space of all totally Ba-measurable functions f:X→E. For a Banach space Y we study the problem of extension of some natural classes of bounded linear operators T:Crc(X,E)→Y to operators T¯:B(Ba,E)→Y.
ISSN:0019-3577
1872-6100
DOI:10.1016/j.indag.2015.07.003