Analysis & PDE
- Anal. PDE
- Volume 8, Number 4 (2015), 1001-1023.
Paving over arbitrary MASAs in von Neumann algebras
We consider a paving property for a maximal abelian -subalgebra (MASA) in a von Neumann algebra , that we call so-paving, involving approximation in the so-topology, rather than in norm (as in classical Kadison–Singer paving). If is the range of a normal conditional expectation, then so-paving is equivalent to norm paving in the ultrapower inclusion . 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 , all Cartan subalgebras in amenable von Neumann algebras and in group measure space II factors arising from profinite actions. By earlier work of Popa, the conjecture also holds true for singular MASAs in II factors, and we obtain here an improved paving size , which we show to be sharp.
Anal. PDE, Volume 8, Number 4 (2015), 1001-1023.
Received: 12 January 2015
Revised: 18 February 2015
Accepted: 25 March 2015
First available in Project Euclid: 16 November 2017
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Popa, Sorin; Vaes, Stefaan. Paving over arbitrary MASAs in von Neumann algebras. Anal. PDE 8 (2015), no. 4, 1001--1023. doi:10.2140/apde.2015.8.1001. https://projecteuclid.org/euclid.apde/1510843118