International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 621386, 7 pages
doi:10.1155/2009/621386
On the Tensor Products of Maximal Abelian JW-Algebras
F.B.H. Jamjoom
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
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.