Copyright © 2009 F. B. H. Jamjoom. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

It is well known in the work of Kadison and Ringrose (1983) that if A and B are maximal abelian von Neumann subalgebras of von Neumann algebras M and N, respectively, then A⊗̅B is a maximal abelian von Neumann subalgebra of M⊗̅N. It is then natural to ask whether a similar result holds in the context of JW-algebras and the JW-tensor product. Guided to some extent by the close relationship between a JW-algebra M and its universal enveloping von Neumann algebra W*(M), we seek in this article to investigate the answer to this question.