A Riesz representation theory for completely regular Hausdorff spaces and its applications

• Autorzy: Marian Nowak
• Języki publikacji: EN

Abstrakty

EN

Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let Cb(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 : Cb(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 : Cb(X, E) → F. As an application, we study (β, || · ||F)-continuous weakly compact and unconditionally converging operators T : Cb(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 (Cb(X, E), β) has the V property of Pełczynski.

Słowa kluczowe

EN

Spaces of vector-valued continuous functions; Strict topologies; Operator measures; Strongly bounded operators; Unconditionally converging operators; Weakly compact operators

Kategorie tematyczne

• 46A70: Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
• 46E40: Spaces of vector- and operator-valued functions
• 46G10: Vector-valued measures and integration

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 474-496

Daty

wydano

2016-01-01

otrzymano

2016-03-13

zaakceptowano

2016-05-31

online

2016-07-29

Twórcy

autor

Marian Nowak

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

Identyfikatory

DOI

10.1515/math-2016-0043