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The centraliser of the injective tensor product

Published online by Cambridge University Press:  17 April 2009

Wend Werner
Wend Werner
Affiliation:
Department of Mathematics, Universität – Gesamthochschule Paderborn, Fachbereich 17 Postfach 1621, Paderborn, Federal Republic of Germany
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Abstract

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The aim of this note is to obtain an intrinsic product formula for the centraliser of the injective tensor product of a couple of Banach spaces, Z(). More precisely, we are going to prove that

Here, the spaces and depend only on X and Y, respectively, and Xk denotes the topological k-product.

A Counterexaple used to demonstrate that the k-product cannot beavoided serves as an answer to a question posed by W. Rueß and D. Werner concerning the behaviour of M-ideals on Y.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 3 , December 1991 , pp. 357 - 365
Copyright
Copyright © Australian Mathematical Society 1991

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