Strong singularity of singular masas in II1 factors

A singular masa A in a II 1 factor N is defined by the property that any unitary w N for which A = wAw* must lie in A. A strongly singular masa A is one that satisfies the inequality ||E A - E wAw* || ,2 ||w - E A (w)|| 2 for all unitaries w N, where E A is the conditional expectation of N onto A, and || || ,2 is defined for bounded maps : N N by sup{||(x)||2 : x N, ||x|| 1}. Strong singularity easily implies singularity, and the main result of this paper shows the reverse implication. 2007 University of Illinois.

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