Constructing MASAs with prescribed properties

Abstract

We consider an iterative procedure for constructing maximal abelian ∗-subalgebras (MASAs) satisfying prescribed properties in II1 factors. This method pairs well with the intertwining by bimodules technique and with properties of the MASA and of the ambient factor that can be described locally. We obtain such a local characterization for II1 factors M that have an s-MASA, A⊂M (i.e., for which A∨JAJ is maximal abelian in B(L2M)), and use this strategy to prove that any factor in this class has uncountably many nonintertwinable singular (resp., semiregular) s-MASAs.