On commutative, operator amenable subalgebras of finite von Neumann algebras
-
Yemon Choi
Abstract
It has been conjectured, motivated in part by old results of Dixmier and Day on bounded Hilbertian representations of amenable groups, that every norm-closed amenable subalgebra of ℬ (ℋ) is automatically similar to an amenable C*-algebra. Results of Curtis and Loy (1995), Gifford (2006), and Marcoux (2008) give some evidence to support this conjecture, but it remains open even for commutative subalgebras.
We present more evidence to support this conjecture, by showing that a closed, commutative, operator amenable subalgebra of a finite von Neumann algebra ℳ must be similar to a selfadjoint-subalgebra. Technical results used include an approximation argument based on Grothendieck's inequality and the Pietsch Domination Theorem, together with an adaptation of a theorem of Gifford to the setting of unbounded operators affiliated to ℳ.
©[2013] by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Deformation of the O'Grady moduli spaces
- Maximal and reduced Roe algebras of coarsely embeddable spaces
- Einstein manifolds and extremal Kähler metrics
- On the limit distributions of some sums of a random multiplicative function
- The index of a transverse Dirac-type operator: the case of abelian Molino sheaf
- Traces on symmetrically normed operator ideals
- On commutative, operator amenable subalgebras of finite von Neumann algebras
- Convergence of the Kähler–Ricci flow on Fano manifolds
Articles in the same Issue
- Deformation of the O'Grady moduli spaces
- Maximal and reduced Roe algebras of coarsely embeddable spaces
- Einstein manifolds and extremal Kähler metrics
- On the limit distributions of some sums of a random multiplicative function
- The index of a transverse Dirac-type operator: the case of abelian Molino sheaf
- Traces on symmetrically normed operator ideals
- On commutative, operator amenable subalgebras of finite von Neumann algebras
- Convergence of the Kähler–Ricci flow on Fano manifolds
