Strong singularity of singular masas in II₁ factors

Sinclair, A.M., Smith, R.R., White, S.A. and Wiggins, A. (2007) Strong singularity of singular masas in II₁ factors. Illinois Journal of Mathematics, 51(4), pp. 1077-1084.

Abstract

A singular masa A in a II₁ 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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: White, Professor Stuart
• Authors: Sinclair, A.M., Smith, R.R., White, S.A., and Wiggins, A.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Illinois Journal of Mathematics
• Publisher: University Of Illinois
• ISSN: 0019-2082
• Copyright Holders: Copyright © 2007 University Of Illinois
• First Published: First published in Illinois Journal of Mathematics 51(4):1077-1084
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher