Strong singularity of singular masas in ${
m II}sb 1$ factors Academic Article uri icon

abstract

  • 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 φ : N → N by sup{||φ(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.

author list (cited authors)

  • Sinclair, A. M., Smith, R. R., White, S. A., & Wiggins, A.

citation count

  • 6

publication date

  • October 2007