Spectrally bounded operators on simple algebras
Author:
Martin Mathieu
Journal:
Proc. Amer. Math. Soc. 132 (2004), 443446
MSC (2000):
Primary 47B48; Secondary 46L05, 47A65, 17C65
Published electronically:
August 7, 2003
MathSciNet review:
2022367
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: A linear mapping from a subspace of a Banach algebra into another Banach algebra is called spectrally bounded if there is a constant such that for all , where 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:
http://dx.doi.org/10.1090/S0002993903072150
PII:
S 00029939(03)072150
Keywords:
Spectrally bounded operators,
Jordan homomorphisms,
purely infinite simple $C^*$algebras
Received by editor(s):
September 30, 2002
Published electronically:
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 Analysis and Operators (HPRNCT200000116)
Communicated by:
David R. Larson
Article copyright:
© Copyright 2003
American Mathematical Society
