On the Tensor Products of Maximal Abelian JW-Algebras

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.