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2015 Paving over arbitrary MASAs in von Neumann algebras
Sorin Popa, Stefaan Vaes
Anal. PDE 8(4): 1001-1023 (2015). DOI: 10.2140/apde.2015.8.1001

Abstract

We consider a paving property for a maximal abelian -subalgebra (MASA) A in a von Neumann algebra M, that we call so-paving, involving approximation in the so-topology, rather than in norm (as in classical Kadison–Singer paving). If A is the range of a normal conditional expectation, then so-paving is equivalent to norm paving in the ultrapower inclusion Aω Mω. We conjecture that any MASA in any von Neumann algebra satisfies so-paving. We use work of Marcus, Spielman and Srivastava to check this for all MASAs in (2), all Cartan subalgebras in amenable von Neumann algebras and in group measure space II1 factors arising from profinite actions. By earlier work of Popa, the conjecture also holds true for singular MASAs in II1 factors, and we obtain here an improved paving size Cε2, which we show to be sharp.

Citation

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Sorin Popa. Stefaan Vaes. "Paving over arbitrary MASAs in von Neumann algebras." Anal. PDE 8 (4) 1001 - 1023, 2015. https://doi.org/10.2140/apde.2015.8.1001

Information

Received: 12 January 2015; Revised: 18 February 2015; Accepted: 25 March 2015; Published: 2015
First available in Project Euclid: 16 November 2017

zbMATH: 1329.46056
MathSciNet: MR3366008
Digital Object Identifier: 10.2140/apde.2015.8.1001

Subjects:
Primary: 46L10
Secondary: 46A22‎ , 46L30

Keywords: Kadison–Singer problem , maximal abelian subalgebra , paving , von Neumann algebra

Rights: Copyright © 2015 Mathematical Sciences Publishers

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