Singular Masas and Measure-Multiplicity Invariant

Details Singular Masas and Measure-Multiplicity Invariant Singular Masas and Measure-Multiplicity Invariant

2011-04-18

arxiv.org/abs/1104.3507v1

Mathematics

Operator Algebras

24 pages, to appear in Houston. J. Math

Scientific paper

In this paper we study relations between the \emph{left-right-measure} and properties of singular masas. Part of the analysis is mainly concerned with masas for which the \emph{left-right-measure} is the class of product measure. We provide examples of Tauer masas in the hyperfinite $\rm{II}_{1}$ factor whose \emph{left-right-measure} is the class of Lebesgue measure. We show that for each subset $S\subseteq \mathbb{N}$, there exist uncountably many pairwise non conjugate singular masas in the free group factors with \emph{Puk\'{a}nszky invariant} $S\cup\{\infty\}$.

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