3 problems

Let $M$ be a von Neumann algebra, let $A\subset M$ be a MASA that is the range of a normal conditional expectation, and let $A^\omega$ denote its ultrapower. For $n\geq 2$ and a se…

Let $T^{(1)}$ and $T^{(2)}$ be weakly mixing free ergodic measure-preserving actions of abelian groups $G_1$ and $G_2$, respectively, and let $S_{T^{(i)}}$ be the singular masas ge…

Let $M$ be a non-amenable II$_1$ factor, and let $A\subset M$ be a maximal abelian self-adjoint subalgebra (MASA). The MASA $A$ is maximal amenable if there is no intermediate amen…