Geodesic
TENSOR PRODUCTS OF MAXIMAL ABELIAN SUBALGBERAS OF C*-ALGEBRAS
Glasgow mathematical journal, Tome 50 (2008) no. 2, pp. 209-216

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.1017/S0017089508004151
Mots-clés : 46L06 
WASSERMANN, SIMON. TENSOR PRODUCTS OF MAXIMAL ABELIAN SUBALGBERAS OF C*-ALGEBRAS. Glasgow mathematical journal, Tome 50 (2008) no. 2, pp. 209-216. doi: 10.1017/S0017089508004151
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