Some Classes of Continuous Operators on Spaces of Bounded Vector-Valued Continuous Functions with the Strict Topology

Let X be a completely regular Hausdorff space and let E , · E and ( F , · 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 σ . We study the relationship between important classes of ( β σ , · F ) -continuou...

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Veröffentlicht in:Journal of function spaces Jg. 2015; H. 2015; S. 1 - 13
1. Verfasser: Nowak, Marian
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cairo, Egypt Hindawi Publishing Corporation 01.01.2015
John Wiley & Sons, Inc
Wiley
Schlagworte:
Banach space
Function space
Linear operators
Operators
Theorems
Topology
ISSN:2314-8896, 2314-8888
Online-Zugang:Volltext
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Zusammenfassung:Let X be a completely regular Hausdorff space and let E , · E and ( F , · 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 σ . We study the relationship between important classes of ( β σ , · F ) -continuous linear operators T : C b ( X , E ) →F (strongly bounded, unconditionally converging, weakly completely continuous, completely continuous, weakly compact, nuclear, and strictly singular) and the corresponding operator measures given by Riesz representing theorems. Some applications concerning the coincidence among these classes of operators are derived.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:2314-8896
2314-8888
DOI:10.1155/2015/796753