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

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 474-496
- ISSN: 2391-5455

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topMarian Nowak. "A Riesz representation theory for completely regular Hausdorff spaces and its applications." Open Mathematics 14.1 (2016): 474-496. <http://eudml.org/doc/285710>.

@article{MarianNowak2016,

abstract = {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.},

author = {Marian Nowak},

journal = {Open Mathematics},

keywords = {Spaces of vector-valued continuous functions; Strict topologies; Operator measures; Strongly bounded operators; Unconditionally converging operators; Weakly compact operators; spaces of vector-valued continuous functions; strict topologies; operator measures; strongly bounded operators; unconditionally converging operators; weakly compact operators},

language = {eng},

number = {1},

pages = {474-496},

title = {A Riesz representation theory for completely regular Hausdorff spaces and its applications},

url = {http://eudml.org/doc/285710},

volume = {14},

year = {2016},

}

TY - JOUR

AU - Marian Nowak

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

JO - Open Mathematics

PY - 2016

VL - 14

IS - 1

SP - 474

EP - 496

AB - 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.

LA - eng

KW - Spaces of vector-valued continuous functions; Strict topologies; Operator measures; Strongly bounded operators; Unconditionally converging operators; Weakly compact operators; spaces of vector-valued continuous functions; strict topologies; operator measures; strongly bounded operators; unconditionally converging operators; weakly compact operators

UR - http://eudml.org/doc/285710

ER -

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