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

 

Splitting for subalgebras of tensor products


Author: Joachim Zacharias
Journal: Proc. Amer. Math. Soc. 129 (2001), 407-413
MSC (2000): Primary 46L06, 46L45
Published electronically: July 27, 2000
MathSciNet review: 1706957
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Abstract:

We prove splitting results for subalgebras of tensor products of operator algebras. In particular, any $C^*$-algebra $C$ s.t. $A\otimes 1 \subseteq C \subseteq A \otimes B$ is a tensor product $A\otimes B_0 $ provided $A$ is simple and nuclear.


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Additional Information

Joachim Zacharias
Affiliation: Département de Mathématiques, UFR Université d’Orléans, Rue de Chartres - BP 6759, 45067 Orléans Cedex 2, France
Address at time of publication: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD England
Email: zacharia@labomath.univ-orleans.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05629-X
PII: S 0002-9939(00)05629-X
Keywords: Tensor products, splitting, slice map property
Received by editor(s): April 9, 1999
Published electronically: July 27, 2000
Additional Notes: This research was supported by the European Community.
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society