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

Juliusz 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 -

References

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