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TENSOR PRODUCTS OF MAXIMAL ABELIAN SUBALGBERAS OF C*-ALGEBRAS

Published online by Cambridge University Press:  01 May 2008

SIMON WASSERMANN
SIMON WASSERMANN*
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, United Kingdom e-mail: asw@maths.gla.ac.uk
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Abstract

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It is shown that if C1 and C2 are maximal abelian self-adjoint subalgebras (masas) of C*-algebras A1 and A2, respectively, then the completion C1 ⊗ C2 of the algebraic tensor product C1 ⊙ C2 of C1 and C2 in any C*-tensor product A1 ⊗βA2 is maximal abelian provided that C1 has the extension property of Kadison and Singer and C2 contains an approximate identity for A2. 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.

Keywords

46L06
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 2 , May 2008 , pp. 209 - 216
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

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