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Mappings which Preserve Idempotents, Local Automorphisms, and Local Derivations

Published online by Cambridge University Press:  20 November 2018

Matej Brešar  and
Peter Šemrl
Matej Brešar
Affiliation:
Department of Mathematics, University of Maribor, PF, Koroška 160, 62000 Maribor, Slovenia
Peter Šemrl
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 19, 61000 Ljubljana, Slovenia
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Abstract

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It is proved that linear mappings of matrix algebras which preserve idempotents are Jordan homomorphisms. Applying this theorem we get some results concerning local derivations and local automorphisms. As an another application, the complete description of all weakly continuous linear surjective mappings on standard operator algebras which preserve projections is obtained. We also study local ring derivations on commutative semisimple Banach algebras.

Keywords

15A0446J9947B4747D30
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 3 , 01 June 1993 , pp. 483 - 496
Copyright
Copyright © Canadian Mathematical Society 1993

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