Search

In the 1970s, Feldman and Moore classified separably acting von Neumann algebras containing Cartan maximal abelian self-adjoint subalgebras (MASAs) using measured equivalence relations and 2-cocycles on such equivalence relations. In this paper we give a new classification in terms of extensions of inverse semigroups. Our approach is more algebraic in character and less point-based than that of Feldman and Moore. As an application, we give a restatement of the spectral theorem for bimodules in terms of subsets of inverse semigroups. We also show how our viewpoint leads naturally to a description of maximal subdiagonal algebras.

We define the Schur multipliers of a separable von Neumann algebra with Cartan maximal abelian self-adjoint algebra , generalizing the classical Schur multipliers of (ℓ2). We characterize these as the normal -bimodule maps on . If contains a direct summand isomorphic to the hyperfinite II1 factor, then we show that the Schur multipliers arising from the extended Haagerup tensor product ⊗eh are strictly contained in the algebra of all Schur multipliers.

Search Results

Refine search

Refine search

Actions for selected content:

3 results

Corrigendum: Von Neumann algebras and extensions of inverse semigroups

Von Neumann Algebras and Extensions of Inverse Semigroups

Schur Multipliers of Cartan Pairs

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

3 results

Corrigendum: Von Neumann algebras and extensions of inverse semigroups

Von Neumann Algebras and Extensions of Inverse Semigroups

Schur Multipliers of Cartan Pairs