Pointwise approximation by elementary complete contractions

Magajna, Bojan

doi:10.1090/S0002-9939-09-09781-0

Pointwise approximation by elementary complete contractions
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Proc. Amer. Math. Soc. 137 (2009), 2375-2385 Request permission

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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