On injective von Neumann algebras
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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.References
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Additional Information
- G. Racher
- Affiliation: Universität Salzburg, Hellbrunnerstrasse 34, A-5020 Salzburg, Austria
- Email: gerhard.racher@sbg.ac.at
- 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
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 139 (2011), 2529-2541
- MSC (2010): Primary 46L10, 46L05, 46M10
- DOI: https://doi.org/10.1090/S0002-9939-2010-10793-1
- MathSciNet review: 2784818