On the Tensor Products of Maximal Abelian JW-Algebras

الملخص EN

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.