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On the Tensor Products of JW-Algebras

Published online by Cambridge University Press:  20 November 2018

Fatmah B. Jamjoom
Fatmah B. Jamjoom*
Affiliation:
Department of Mathematics, King Saud University, Riyadh, Saudi Arabia
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Abstract

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In this article we introduce and develop a theory of tensor products of JW-algebras. Since JW-algebras are so close to W*-algebras, one can expect that the W*-algebra tensor product theory will be actively involved. It is shown that if Mand N are JW-algebras with centres Z1 and Z2 respectively, then Z1 ⊗ Z2 is not the centre of the JW-tensor product JW() (see below for notation) ofMand N, in general. Also, the type decomposition of JW() has been determined in terms of the type decomposition of the JW-algebras M and N which, essentially, rely on the relationship between the types of the JW-algebra and the types of its universal enveloping Von Neumann algebra.

Keywords

46L1046L0546D25
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 4 , 01 August 1995 , pp. 786 - 800
Copyright
Copyright © Canadian Mathematical Society 1995

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