## Kyoto Journal of Mathematics

### Constructing MASAs with prescribed properties

Sorin Popa

#### 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 s-MASA, $A\subset M$ (i.e., for which $A\veeJAJ$ is maximal abelian in $\mathcal {B}(L^{2}M)$), and use this strategy to prove that any factor in this class has uncountably many nonintertwinable singular (resp., semiregular) s-MASAs.

#### Article information

Source
Kyoto J. Math., Volume 59, Number 2 (2019), 367-397.

Dates
Revised: 5 March 2017
Accepted: 9 March 2017
First available in Project Euclid: 27 February 2019

https://projecteuclid.org/euclid.kjm/1551236641

Digital Object Identifier
doi:10.1215/21562261-2019-0003

Mathematical Reviews number (MathSciNet)
MR3960298

Zentralblatt MATH identifier
07080109

#### Citation

Popa, Sorin. Constructing MASAs with prescribed properties. Kyoto J. Math. 59 (2019), no. 2, 367--397. doi:10.1215/21562261-2019-0003. https://projecteuclid.org/euclid.kjm/1551236641

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