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Uniform approximation by elementary operators

Part of: Special classes of linear operators Selfadjoint operator algebras

Published online by Cambridge University Press:  23 September 2009

Bojan Magajna
Bojan Magajna
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 21, Ljubljana 1000, Slovenia; Email: (bojan.magajna@fmf.uni-lj.si)
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Abstract

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On a separable C*-algebra A every (completely) bounded map which preserves closed two-sided ideals can be approximated uniformly by elementary operators if and only if A is a finite direct sum of C*-algebras of continuous sections vanishing at ∞ of locally trivial C*-bundles of finite type.

Keywords

C*-algebrasubhomogeneousidealselementary operators

MSC classification

Secondary: 46L05: General theory of $C^*$-algebras 46L07: Operator spaces and completely bounded maps 47B47: Commutators, derivations, elementary operators, etc.
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 3 , October 2009 , pp. 731 - 749
Copyright
Copyright © Edinburgh Mathematical Society 2009