Tensor products of maximal Abelian subalgebras of C*-algebras

Wassermann, S. (2008) Tensor products of maximal Abelian subalgebras of C*-algebras. Glasgow Mathematical Journal, 50(2), pp. 209-216. (doi: 10.1017/S0017089508004151)

Abstract

It is shown that if C_1 and C_2 are maximal abelian self-adjoint subalgebras (masas) of C*-algebras A_1 and A_2, respectively, then the completion of the algebraic tensor product of C_1 and C_2 in any C*-tensor product of A_1 and A_2 is maximal abelian provided that C_1 has the extension property of Kadison and Singer and C_2 contains an approximate identity for A_2. Examples are given to show that this result can fail if the conditions on the two masas do not both hold. This gives an answer to a long-standing question, but leaves open some other interesting problems, one of which turns out to have a potentially intriguing implication for the Kadison-Singer extension problem.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Wassermann, Dr Alexander
• Authors: Wassermann, S.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Glasgow Mathematical Journal
• Publisher: Cambridge University Press
• ISSN: 0017-0895
• Published Online: 01 January 2007