The weak Gelfand-Phillips property in spaces of compact operators

Ghenciu, Ioana

Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 1, pp. 35-47.

Résumé

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.

Détail

DOI : 10.14712/1213-7243.2015.195

Classification : 46B20, 46B25, 46B28
Keywords: Grothendieck sets; property $wGP$