A note on invertibility preservers on Banach algebras
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- by Matej Brešar, Ajda Fošner and Peter Šemrl PDF
- Proc. Amer. Math. Soc. 131 (2003), 3833-3837 Request permission
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.References
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Additional Information
- Matej Brešar
- Affiliation: Department of Mathematics, University of Maribor, PF, Koroška 160, SI-2000 Maribor, Slovenia
- Email: bresar@uni-mb.si
- Ajda Fošner
- Affiliation: Department of Mathematics, University of Maribor, PF, Koroška 160, SI-2000 Maribor, Slovenia
- Email: ajda.fosner@uni-mb.si
- Peter Šemrl
- Affiliation: Department of Mathematics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
- Email: peter.semrl@fmf.uni-lj.si
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3833-3837
- MSC (2000): Primary 46H05, 46H10, 47B48
- DOI: https://doi.org/10.1090/S0002-9939-03-07192-2
- MathSciNet review: 1999931