On the Tensor Products of Maximal Abelian J W -Algebras

It is well known in the work of Kadison and Ringrose (1983)that if ð ´ and ð µ are maximal abelian von Neumann subalgebras of von Neumann algebras ð ‘€ and ð ‘ , respectively, then ð ´ âŠ— ð µ is a maximal abelian von Neumann subalgebra of ð ‘€ ⊗ ð ‘ . It is then natural to ask whether a similar result holds in the context of ð ½ ð ‘Š -algebras and the ð ½ ð ‘Š -tensor product. Guided to some extent by the close relationship between a ð ½ ð ‘Š -algebra M and its universal enveloping von Neumann algebra ð ‘Š ∗ ( ð ‘€ ) , we seek in this article to investigate the answer to this question.