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Strong Singularity of Singular Masas in II_1 Factors

Allan Sinclair·Roger Smith·Stuart White·Alan Wiggins
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Abstract

A singular masa $A$ in a $\rm{II}_{1}$ factor $N$ is defined by the property that any unitary $w\in N$ for which $A=wAw^*$ must lie in $A$. A strongly singular masa $A$ is one that satisfies the inequality $$\| E_A- E_{wAw^*}\|_{\infty,2}\geq\|w- E_A(w)\|_2$$ for all unitaries $w\in N$, where $E_A$ is the conditional expectation of $N$ onto $A$, and $\|\cdot\|_{\infty,2}$ is defined for bounded maps $ϕ:N\to N$ by $\sup\{\|ϕ(x)\|_2:x\in N, \|x\|\leq 1\}$. Strong singularity easily implies singularity, and the main result of this paper shows the reverse implication.

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Allan Sinclair, Roger Smith, Stuart White, Alan Wiggins. 2006-01-24. Strong Singularity of Singular Masas in II_1 Factors. https://arxiv.org/abs/math/0601594

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