Some isomorphic properties in $K(X,Y)$ and in projective tensor products
Volume 146 / 2017
Colloquium Mathematicum 146 (2017), 239-252
MSC: Primary 46B20, 46B28, 46M05.
DOI: 10.4064/cm6184-12-2015
Published online: 7 October 2016
Abstract
We study the (DPrcp) property and the Gelfand–Phillips properties in spaces of compact operators. Moreover we give some sufficient conditions implying that the projective tensor product of two Banach spaces is sequentially right (SR) or has the L-limited property. We introduce the dual (SR$^*$) property and we give a characterization of it, also showing that it is intermediate between the (V$^*)$ and the (RDP$^*)$ properties. Finally, we study the Bourgain–Diestel property (BD) and the (RDP$^*)$ property in the space $K_{w^*\hbox {-}w}(X^*,Y).$
