Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Martin Mathieu
Journal: Proc. Amer. Math. Soc. 132 (2004), 443-446
MSC (2000): Primary 47B48; Secondary 46L05, 47A65, 17C65
Published electronically: August 7, 2003
MathSciNet review: 2022367
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A linear mapping $T$ from a subspace $E$ 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 $C^*$-algebra onto a unital semisimple Banach algebra is a Jordan epimorphism.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B48, 46L05, 47A65, 17C65

Retrieve articles in all journals with MSC (2000): 47B48, 46L05, 47A65, 17C65


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/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
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 (HPRN-CT-2000-00116)
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society