International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 621386, 7 pages
Research Article

On the Tensor Products of Maximal Abelian JW-Algebras

Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received 24 April 2009; Accepted 7 June 2009

Academic Editor: Jie Xiao

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.


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 A̅B is a maximal abelian von Neumann subalgebra of M̅N. 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.