The weak Gelfand-Phillips property in spaces of compact operators

Ioana Ghenciu

Commentationes Mathematicae Universitatis Carolinae (2017)

  • Volume: 58, Issue: 1, page 35-47
  • ISSN: 0010-2628

Abstract

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For Banach spaces X and Y , let K w * ( X * , Y ) denote the space of all w * - w continuous compact operators from X * to Y endowed with the operator norm. A Banach space X has the w G P property if every Grothendieck subset of X is relatively weakly compact. In this paper we study Banach spaces with property w G P . We investigate whether the spaces K w * ( X * , Y ) and X ⊗ ϵ Y have the w G P property, when X and Y have the w G P property.

How to cite

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Ghenciu, Ioana. "The weak Gelfand-Phillips property in spaces of compact operators." Commentationes Mathematicae Universitatis Carolinae 58.1 (2017): 35-47. <http://eudml.org/doc/287925>.

@article{Ghenciu2017,
abstract = {For Banach spaces $X$ and $Y$, let $K_\{w^*\}(X^*,Y)$ denote the space of all $w^* - w$ continuous compact operators from $X^*$ to $Y$ endowed with the operator norm. A Banach space $X$ has the $wGP$ property if every Grothendieck subset of $X$ is relatively weakly compact. In this paper we study Banach spaces with property $wGP$. We investigate whether the spaces $K_\{w^*\}(X^*, Y)$ and $X\otimes _\epsilon Y$ have the $wGP$ property, when $X$ and $Y$ have the $wGP$ property.},
author = {Ghenciu, Ioana},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Grothendieck sets; property $wGP$},
language = {eng},
number = {1},
pages = {35-47},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The weak Gelfand-Phillips property in spaces of compact operators},
url = {http://eudml.org/doc/287925},
volume = {58},
year = {2017},
}

TY - JOUR
AU - Ghenciu, Ioana
TI - The weak Gelfand-Phillips property in spaces of compact operators
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 1
SP - 35
EP - 47
AB - For Banach spaces $X$ and $Y$, let $K_{w^*}(X^*,Y)$ denote the space of all $w^* - w$ continuous compact operators from $X^*$ to $Y$ endowed with the operator norm. A Banach space $X$ has the $wGP$ property if every Grothendieck subset of $X$ is relatively weakly compact. In this paper we study Banach spaces with property $wGP$. We investigate whether the spaces $K_{w^*}(X^*, Y)$ and $X\otimes _\epsilon Y$ have the $wGP$ property, when $X$ and $Y$ have the $wGP$ property.
LA - eng
KW - Grothendieck sets; property $wGP$
UR - http://eudml.org/doc/287925
ER -

References

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