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

 

A note on invertibility preservers on Banach algebras


Authors: Matej Bresar, Ajda Fosner and Peter Semrl
Journal: Proc. Amer. Math. Soc. 131 (2003), 3833-3837
MSC (2000): Primary 46H05, 46H10, 47B48
Published electronically: July 9, 2003
MathSciNet review: 1999931
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Abstract: Let ${\mathcal{A}}$ be ${\mathcal{B}}$be semisimple Banach algebras and let $\phi:\mathcal{A}\to\mathcal{B}$be a unital bijective linear operator that preserves invertibility. If the socle of ${\mathcal A}$ is an essential ideal of ${\mathcal A}$, then $\phi$ is a Jordan isomorphism.


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Additional Information

Matej Bresar
Affiliation: Department of Mathematics, University of Maribor, PF, Koroška 160, SI-2000 Maribor, Slovenia
Email: bresar@uni-mb.si

Ajda Fosner
Affiliation: Department of Mathematics, University of Maribor, PF, Koroška 160, SI-2000 Maribor, Slovenia
Email: ajda.fosner@uni-mb.si

Peter Semrl
Affiliation: Department of Mathematics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
Email: peter.semrl@fmf.uni-lj.si

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07192-2
PII: S 0002-9939(03)07192-2
Received by editor(s): July 25, 2002
Published electronically: July 9, 2003
Additional Notes: Partially supported by a grant from the Ministry of Science of Slovenia
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society