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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A criterion for splitting $C^{*}$-algebras
in tensor products


Author: László Zsidó
Journal: Proc. Amer. Math. Soc. 128 (2000), 2001-2006
MSC (1991): Primary 46L05
Published electronically: November 23, 1999
MathSciNet review: 1654056
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Abstract: The goal of the paper is to prove the following theorem: if $A$,$D$ are unital $C^{*}$-algebras, $A$ simple and nuclear, then any $C^{*}$-subalgebra of the $C^{*}$-tensor product of $A$ and $D$, which contains the tensor product of $A$ with the scalar multiples of the unit of $D$, splits in the $C^{*}$-tensor product of $A$ with some $C^{*}$-subalgebra of $D$.


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Additional Information

László Zsidó
Affiliation: Department of Mathematics, University of Rome “Tor Vergata", Via della Ricerca Scientifica, 00133 Rome, Italy
Email: zsido@axp.mat.uniroma2.it

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05269-7
PII: S 0002-9939(99)05269-7
Received by editor(s): August 22, 1998
Published electronically: November 23, 1999
Additional Notes: The author was supported by M.U.R.S.T., C.N.R. and E.U
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society