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Pointwise approximation by elementary complete contractions

Author(s): Bojan Magajna
Journal: Proc. Amer. Math. Soc. 137 (2009), 2375-2385.
MSC (2000): Primary 46L06, 46L07; Secondary 47B47
Posted: January 29, 2009
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Abstract: A complete contraction on a $ C^*$-algebra $ A$, which preserves all closed two sided ideals $ J$, can be approximated pointwise by elementary complete contractions if and only if the induced map on $ B\otimes A/J$ is contractive for every $ C^*$-algebra $ B$, ideal $ J$ in $ A$ and $ C^*$-tensor norm on $ B\otimes A/J$. A lifting obstruction for such an approximation is also obtained.

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Additional Information:

Bojan Magajna
Affiliation: Department of Mathematics, University of Ljubljana, Jadranska 21, Ljubljana 1000, Slovenia
Email: Bojan.Magajna@fmf.uni-lj.si

DOI: 10.1090/S0002-9939-09-09781-0
PII: S 0002-9939(09)09781-0
Keywords: $C^*$-algebra, $C^*$-tensor products, ideals, elementary operators, point norm topology
Received by editor(s): October 18, 2007,
Received by editor(s) in revised form: September 27, 2008
Posted: January 29, 2009
Communicated by: Marius Junge
Copyright of article: Copyright 2009, American Mathematical Society

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