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.



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A singular masa A in a II1 factor N is defined by the property that any unitary wN for which A=wAw* must lie in A. A strongly singular masa A is one that satisfies the inequality ||EA- EwAw*||∞,2 ≥||w- EA(w)||2 for all unitaries wN where EA is the conditional expectation of N onto A, and ||⋅||∞,2 is defined for bounded maps Φ : NN 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
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
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

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