On the normalizing algebra of a MASA in a II${}_1$ Factor

Abstract

Let $A$ be a maximal abelian subalgebra (MASA) in a \II1 factor $M$. Sorin Popa introduced an analytic condition that can be used to identify the normalizing algebra of $A$ in $M$ and which we call \emph{the relative weak asymptotic homomorphism property}. In this paper we show this property is always satisfied by the normalizing algebra of $A$ in $M$ and as a consequence we obtain that ${\overline{⨂}}_{i\in I}({\mathcal{N}}_{M_i}(A_i{)}^{\prime \prime })=({\mathcal{N}}_{{\overline{⨂}}_{i\in I}{M}_i}(\bar{\otimes }$ .

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References in corpus (3)

• On a Class of Type II${}_1$ Factors with Betti Numbers Invariants
• Strong Singularity of Singular Masas in II_1 Factors
• Amalgamated Free Products of $w$-Rigid Factors and Calculation of their Symmetry Groups

Cited by in corpus (7)

• Groupoid normalizers of tensor products
• Strong Singularity for Subfactors
• Masas and Bimodule Decompositions of ${\mathrm{II}}_1$ Factors
• The Takesaki equivalence relation for maximal abelian subalgebras
• The Relative Weak Asymptotic Homomorphism Property for Inclusions of Finite von Neumann Algebras
• On the Relative Weak Asymptotic Homomorphism Property for Triples of Groups von Neumann Algebras
• Normalizers of Irreducible Subfactors