English

Masas and Bimodule Decompositions of $\rm{II}_{1}$ Factors

Operator Algebras 2008-12-09 v1

Abstract

The measure-multiplicity-invariant for masas in II1\rm{II}_{1} factors was introduced in \cite{MR2261688} to distinguish masas that have the same Puk\'{a}nszky invariant. In this paper we study the measure class in the measure-multiplicity-invariant. This is equivalent to studying the standard Hilbert space as an associated bimodule. We characterize the type of any masa depending on the left-right-measure using Baire category methods (selection principle of Jankov and von Neumann). We present a second proof of Chifan's result on normalisers and a measure theoretic proof of the equivalence of weak asymptotic homomorphism property (WAHP) and singularity that appeared in \cite{MR2417416}.

Keywords

Cite

@article{arxiv.0812.1257,
  title  = {Masas and Bimodule Decompositions of $\rm{II}_{1}$ Factors},
  author = {Kunal Mukherjee},
  journal= {arXiv preprint arXiv:0812.1257},
  year   = {2008}
}