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ISSN 1088-6826(e) ISSN 0002-9939(p)

Spectrally bounded operators on simple $C^{*}$ -algebras

Author(s): Martin Mathieu
Journal: Proc. Amer. Math. Soc. 132 (2004), 443-446.
MSC (2000): Primary 47B48; Secondary 46L05, 47A65, 17C65
Posted: August 7, 2003
MathSciNet review: 2022367
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Abstract: A linear mapping from a subspace of a Banach algebra into another Banach algebra is called spectrally bounded if there is a constant $M\geq 0$ such that $r(Tx)\leq M\,r(x)$ for all $x\in E$ , where $r(\,\cdot \,)$ denotes the spectral radius. We prove that every spectrally bounded unital operator from a unital purely infinite simple -algebra onto a unital semisimple Banach algebra is a Jordan epimorphism.

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Additional Information:

Martin Mathieu
Affiliation: Department of Pure Mathematics, Queen's University Belfast, Belfast BT7 1NN, Northern Ireland
Email: m.m@qub.ac.uk

DOI: 10.1090/S0002-9939-03-07215-0
PII: S 0002-9939(03)07215-0
Keywords: Spectrally bounded operators, Jordan homomorphisms, purely infinite simple $C^*$-algebras
Received by editor(s): September 30, 2002
Posted: August 7, 2003
Additional Notes: This paper was written during a visit to the Departamento de Análisis Matemático de la Universidad de Granada, Granada, Spain. The author gratefully acknowledges the generous hospitality extended to him by his colleagues there. The paper is part of the research carried out in the EC network {\em Analysis and Operators\/} (HPRN-CT-2000-00116)
Communicated by: David R. Larson
Copyright of article: Copyright 2003, American Mathematical Society

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