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Elementary operators and subhomogeneous C*-algebras

Part of: Selfadjoint operator algebras Special classes of linear operators

Published online by Cambridge University Press:  28 October 2010

Ilja Gogić
Ilja Gogić
Affiliation:
Department of Mathematics, University of Zagreb, Bijenička cesta 30, Zagreb 10000, Croatia ([email protected])
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Abstract

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Let A be a C*-algebra and let ΘA be the canonical contraction form the Haagerup tensor product of M(A) with itself to the space of completely bounded maps on A. In this paper we consider the following conditions on A: (a) A is a finitely generated module over the centre of M(A); (b) the image of ΘA is equal to the set E(A) of all elementary operators on A; and (c) the lengths of elementary operators on A are uniformly bounded. We show that A satisfies (a) if and only if it is a finite direct sum of unital homogeneous C*-algebras. We also show that if a separable A satisfies (b) or (c), then A is necessarily subhomogeneous and the C*-bundles corresponding to the homogeneous subquotients of A must be of finite type.

Keywords

C*-algebrasubhomogeneouselementary 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 54 , Issue 1 , February 2011 , pp. 99 - 111
Copyright
Copyright © Edinburgh Mathematical Society 2010

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