Vol. 36, No. 1, 1971

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Hilbertian operators and reflexive tensor products

James R. Holub

Vol. 36 (1971), No. 1, 185–194
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 πY,X 𝜖Y , and (X,Y ) to be reflexive are given, and examples of infinite dimensional spaces X and Y for which X πY,X 𝜖Y , and 2(X,Y ) are reflexive are constructed.

Mathematical Subject Classification 2000
Primary: 46B10
Secondary: 47B10
Milestones
Received: 2 October 1969
Published: 1 January 1971
Authors
James R. Holub