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

 

On injective von Neumann algebras


Author: G. Racher
Journal: Proc. Amer. Math. Soc. 139 (2011), 2529-2541
MSC (2010): Primary 46L10, 46L05, 46M10
Published electronically: December 21, 2010
MathSciNet review: 2784818
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Abstract: Partially answering a question of A.Ya. Helemskii, we show that a von Neumann algebra is injective if and only if all its normal dual Banach left modules are $ 1$-injective in the sense of the homology of Banach algebras. Nuclear $ C^*$-algebras are characterized in a similar manner.


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Additional Information

G. Racher
Affiliation: Universität Salzburg, Hellbrunnerstrasse 34, A-5020 Salzburg, Austria
Email: gerhard.racher@sbg.ac.at

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10793-1
PII: S 0002-9939(2010)10793-1
Keywords: Injective von Neumann algebras, nuclear $C^{*}$-algebras, injective Banach modules.
Received by editor(s): November 13, 2009
Received by editor(s) in revised form: July 9, 2010
Published electronically: December 21, 2010
Communicated by: Marius Junge
Article copyright: © Copyright 2010 American Mathematical Society