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.
Keywords: Grothendieck sets; property $wGP$
DOI: DOI 10.14712/1213-7243.2015.195
AMS Subject Classification: 46B20 46B25 46B28