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arXiv · 1610.08945

Constructing MASAs with prescribed properties

Sorin Popa
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Abstract

We consider an iterative procedure for constructing maximal abelian $^*$-subalgebras (MASAs) satisfying prescribed properties in II$_1$ 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 II$_1$ factors $M$ that have an {\it s-MASA}, $A\subset M$ (i.e., for which $A \vee JAJ$ is maximal abelian in $\Cal B(L^2M)$), and use this strategy to prove that any factor in this class has uncountably many non-intertwinable singular (respectively semiregular) s-MASAs.

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Sorin Popa. 2016-10-27. Constructing MASAs with prescribed properties. https://doi.org/10.1215/21562261-2019-0003

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