## Strong singularity of singular masas in II_{1} factors

*Abstract:* A singular masa A in a 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 \phi :N\to N by \sup\{\|\phi(x)\|_2:x\in N, \|x\|\leq 1\}. Strong singularity easily implies singularity, and the main result of this paper shows the reverse implication.

### Publication Details

*Coauthors:* Allan Sinclair, Roger Smith and Alan Wiggins.

llinois J. Math. 51 (4) 2007, 1077-1084.

*Download:* Journal Website, arXiv.math:0601594, Glasgow ePrint 4610.

The versions on the arXiv and the Glasgow ePrint server are those accepted by the journal.

## Just after a 24 hour bike relay

A surprisingly hot day in October 2010 in Fort William made the bike relay much more enjoyable than anticipated. I'd even think about another one.