Strong singularity of singular masas in ${\rm II}\sb 1$ factors
Sinclair, Allan M. ; Smith, Roger R. ; White, Stuart A. ; Wiggins, Alan
Illinois J. Math., Tome 51 (2007) no. 3, p. 1077-1084 / Harvested from Project Euclid
A singular masa $A$ in a ${\mathrm{II}}_1$ 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 ¶ \[ \|\bb E_A-\bb E_{wAw^*}\|_{\infty,2}\geq\|w-\bb E_A(w)\|_2 \] ¶ for all unitaries $w\in N$, where $\bb E_A$ 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.
Publié le : 2007-10-15
Classification:  46L10,  46L35
@article{1258138533,
     author = {Sinclair, Allan M. and Smith, Roger R. and White, Stuart A. and Wiggins, Alan},
     title = {Strong singularity of singular masas in ${\rm II}\sb 1$ factors},
     journal = {Illinois J. Math.},
     volume = {51},
     number = {3},
     year = {2007},
     pages = { 1077-1084},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138533}
}
Sinclair, Allan M.; Smith, Roger R.; White, Stuart A.; Wiggins, Alan. Strong singularity of singular masas in ${\rm II}\sb 1$ factors. Illinois J. Math., Tome 51 (2007) no. 3, pp.  1077-1084. http://gdmltest.u-ga.fr/item/1258138533/