A note on spectrum-preserving maps

Let A and B be unital semisimple Banach algebras. If ϕ : M 2 ( A ) → B is a bijective spectrum-preserving linear map, then ϕ is a Jordan homomorphism.

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Bibliographic Details
Published in:	Journal of mathematical analysis and applications Vol. 387; no. 2; pp. 595 - 603
Main Authors:	Alaminos, J., Brešar, M., Šemrl, P., Villena, A.R.
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15-03-2012
Subjects:	Banach algebra Jordan homomorphism Spectrum-preserving map Spectrum-preserving map Jordan homomorphism Banach algebra
Online Access:	Get full text
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Description
Summary:	Let A and B be unital semisimple Banach algebras. If ϕ : M 2 ( A ) → B is a bijective spectrum-preserving linear map, then ϕ is a Jordan homomorphism.
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2011.09.024