On the tensor products of maximal abelian JW-algebras (Q1035168)

Summary: It is well-known from the work of Kadison and Ringrose that, if \(A\) and \(B\) are maximal abelian von~Neumann subalgebras of von~Neumann algebras \(M\) and \(N\), respectively, then \(A \overline {\otimes} B\) is a maximal abelian von~Neumann subalgebra of \(M\overline \otimes N\). 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.