Groupoid normalizers of tensor products

Fang, J., Smith, R., White, S.A. and Wiggins, A.D. (2010) Groupoid normalizers of tensor products. Journal of Functional Analysis, 258(1), pp. 20-49. (doi: 10.1016/j.jfa.2009.10.005)

Abstract

We consider an inclusion B [subset of or equal to] M of finite von Neumann algebras satisfying B′∩M [subset of or equal to] B. A partial isometry vset membership, variantM is called a groupoid normalizer if vBv*,v*Bv[subset of or equal to] B. Given two such inclusions B_i [subset of or equal to] M_i, i=1,2, we find approximations to the groupoid normalizers of [formula] in [formula], from which we deduce that the von Neumann algebra generated by the groupoid normalizers of the tensor product is equal to the tensor product of the von Neumann algebras generated by the groupoid normalizers. Examples are given to show that this can fail without the hypothesis [formula], i=1,2. We also prove a parallel result where the groupoid normalizers are replaced by the intertwiners, those partial isometries vset membership, variantM satisfying vBv*[subset of or equal to] B and v*v,vv*[set membership, variant] B.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: White, Professor Stuart
• Authors: Fang, J., Smith, R., White, S.A., and Wiggins, A.D.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Functional Analysis
• Publisher: Elsevier
• ISSN: 0022-1236
• Copyright Holders: Copyright © 2010 Elsevier