Vol. 81, No. 2, 1979

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ISSN: 0030-8730
The centralizer of tensor products of Banach spaces (a function space representation)

Ehrhard Behrends

Vol. 81 (1979), No. 2, 291–301
Abstract

Let X, Y be real Banach spaces, X𝜖Y their usual 𝜖-tensor product. We represent Z(X𝜖Y ), the centralizer of X𝜖Y , as a space of real-valued functions on a suitable compact Hausdorff space. As a corollary we obtain Wickstead’s result: Z(X𝜖Y ) is the closure with respect to the strong operator topology of Z(X) Z(Y ). In addition it is shown that Z(X𝜖Y ) is in fact the uniform closure of Z(X) Z(Y ) provided the norm topology and the strong operator topology coincide on the centralizers of X and Y .

Mathematical Subject Classification 2000
Primary: 46M05
Milestones
Received: 15 September 1977
Revised: 5 May 1978
Published: 1 April 1979
Authors
Ehrhard Behrends