On Ozawa's Property for Free Group Factors
Sorin Popa
TL;DR
This paper provides a new proof that certain subalgebras within free group factors are amenable if their relative commutant is diffuse, enhancing understanding of the structure of these von Neumann algebras.
Contribution
It offers a novel proof of Ozawa's result on the amenability of subalgebras with diffuse relative commutant in free group factors.
Findings
Subalgebras with diffuse relative commutant are amenable.
New proof simplifies understanding of Ozawa's original result.
Strengthens the structural theory of free group factors.
Abstract
We give a new proof of a result of Ozawa showing that if a von Neumann subalgebra of a free group factor has relative commutant diffuse (i.e. without atoms), then is amenable.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Algebraic structures and combinatorial models