# Weakly precompact operators on ${C}_{b}(X,E)$ with the strict topology

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2016)

- Volume: 36, Issue: 1, page 65-77
- ISSN: 1509-9407

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topJuliusz Stochmal. "Weakly precompact operators on $C_{b}(X,E)$ with the strict topology." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 36.1 (2016): 65-77. <http://eudml.org/doc/286883>.

@article{JuliuszStochmal2016,

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 study weakly precompact operators $T:C_\{b\}(X,E) → F$. In particular, we show that if X is a paracompact k-space and E contains no isomorphic copy of l¹, then every strongly bounded operator $T:C_\{b\}(X,E) → F$ is weakly precompact.},

author = {Juliusz Stochmal},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {spaces of vector-valued continuous functions; strict topologies; operator measures; strongly bounded operators; weakly precompact operators},

language = {eng},

number = {1},

pages = {65-77},

title = {Weakly precompact operators on $C_\{b\}(X,E)$ with the strict topology},

url = {http://eudml.org/doc/286883},

volume = {36},

year = {2016},

}

TY - JOUR

AU - Juliusz Stochmal

TI - Weakly precompact operators on $C_{b}(X,E)$ with the strict topology

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2016

VL - 36

IS - 1

SP - 65

EP - 77

AB - 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 study weakly precompact operators $T:C_{b}(X,E) → F$. In particular, we show that if X is a paracompact k-space and E contains no isomorphic copy of l¹, then every strongly bounded operator $T:C_{b}(X,E) → F$ is weakly precompact.

LA - eng

KW - spaces of vector-valued continuous functions; strict topologies; operator measures; strongly bounded operators; weakly precompact operators

UR - http://eudml.org/doc/286883

ER -

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