Pointwise approximation by elementary complete contractions
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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.References
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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
- Received by editor(s): October 18, 2007
- Received by editor(s) in revised form: September 27, 2008
- Published electronically: January 29, 2009
- Communicated by: Marius Junge
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 2375-2385
- MSC (2000): Primary 46L06, 46L07; Secondary 47B47
- DOI: https://doi.org/10.1090/S0002-9939-09-09781-0
- MathSciNet review: 2495272