On commutative, operator amenable subalgebras of finite von Neumann algebras

Details On commutative, operator amenable subalgebras of finite von Neumann algebras On commutative, operator amenable subalgebras of finite von Neumann algebras

2010-12-20

arxiv.org/abs/1012.4259v3

Mathematics

Operator Algebras

v3: 20 pages, 2 figures, uses Paul Taylor's diagrams.sty macros. New version avoids use or mention of the conditional unitizat

Scientific paper

An open question, raised independently by several authors, asks if a closed amenable subalgebra of ${\mathcal B}({\mathcal H})$ must be similar to an amenable C*-algebra; the question remains open even for singly-generated algebras. In this article we show that any closed, commutative, operator amenable subalgebra of a finite von Neumann algebra ${\mathcal M}$ is similar to a commutative C*-subalgebra of ${\mathcal M}$, with the similarity implemented by an element of ${\mathcal M}$. Our proof makes use of the algebra of measurable operators affiliated to ${\mathcal M}$.

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