Hilbertian operators and reflexive tensor products

James R. Holub

Vol. 36 (1971), No. 1, 185–194

DOI: 10.2140/pjm.1971.36.185

Abstract

This paper is a study of reflexivity of tensor products of Banach spaces and the related topic of reflexivity of the space ℒ(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 ℒ(X,Y ) to be reflexive are given, and examples of infinite dimensional spaces X and Y for which X ⊗_πY,X ⊗_𝜖Y , and ℒ²(X,Y ) are reflexive are constructed.

Mathematical Subject Classification 2000

Primary: 46B10

Secondary: 47B10

Milestones

Received: 2 October 1969

Published: 1 January 1971