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- W2499458511 abstract "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 develop the Riemman-Stieltjes-type Integral representation theory of ( β , || · || F ) -continuous operators T : C b ( X , E ) → F with respect to the representing Borel operator measures. For X being a k -space, we characterize strongly bounded ( β , || · || F )-continuous operators T : C b ( X , E ) → F . As an application, we study ( β , || · || F )-continuous weakly compact and unconditionally converging operators T : C b ( X , E ) → F . In particular, we establish the relationship between these operators and the corresponding Borel operator measures given by the Riesz representation theorem. We obtain that if X is a k -spaceand E is reflexive, then ( C b ( X , E ), β ) has the V property of Pełczynski." @default.
- W2499458511 created "2016-08-23" @default.
- W2499458511 creator A5029667253 @default.
- W2499458511 date "2016-01-01" @default.
- W2499458511 modified "2023-10-09" @default.
- W2499458511 title "A Riesz representation theory for completely regular Hausdorff spaces and its applications" @default.
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- W2499458511 doi "https://doi.org/10.1515/math-2016-0043" @default.
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