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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Spectral isometries on non-simple C*-algebras


Authors: Martin Mathieu and Ahmed R. Sourour
Journal: Proc. Amer. Math. Soc. 142 (2014), 129-135
MSC (2010): Primary 47A65, 47A10, 47B48, 46H10, 46L05
Published electronically: August 27, 2013
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Abstract: We prove that unital surjective spectral isometries on certain non-simple unital C*-algebras are Jordan isomorphisms. Along the way, we establish several general facts in the setting of semisimple Banach algebras.


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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

Ahmed R. Sourour
Affiliation: Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3R4
Email: sourour@math.uvic.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11704-1
PII: S 0002-9939(2013)11704-1
Keywords: Spectral isometries, spectrally bounded operators, Jordan isomorphisms, C*-algebras
Received by editor(s): July 25, 2011
Received by editor(s) in revised form: February 16, 2012
Published electronically: August 27, 2013
Additional Notes: This paper was written during a visit of the first-named author to the University of Victoria in May 2011, supported by a Research in Pairs grant of the London Mathematical Society
The second-named author’s research was supported by an NSERC Discovery Grant
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2013 American Mathematical Society