Hilbertian operators and reflexive tensor products

Abstract

This paper is a study of reflexivity of tensor products of Banach spaces and the related topic of reflexivity of the space ?{X, Y) (the space of bounded linear operators from X to Y with operator norm). If X and Y are Banach spaces with Schauder bases, then necessary and sufficient conditions for X(g) Y, X(g) , and <f(X, Y) to be reflexive are given, and examples of infinite dimensional spaces X and Y for which X x Y, X(g) Y, and f(X, Y) are reflexive are constructed.