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Derivations mapping into the socle, II

Author: Matej Bresar
Journal: Proc. Amer. Math. Soc. 126 (1998), 181-187
MSC (1991): Primary 46H05
MathSciNet review: 1416078
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Abstract: Let $\mathcal A$ be a unital Banach algebra. Several characterizations of continuous derivations of $\mathcal A$ having only elements with finite spectrum in their ranges are obtained. In particular, if $\mathcal A$ is semisimple, then such derivations map $\mathcal A$ into its socle.

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Matej Bresar
Affiliation: Department of Mathematics, University of Maribor, PF, Koroška 160, 62000 Maribor, Slovenia

Received by editor(s): March 20, 1996
Received by editor(s) in revised form: July 8, 1996
Additional Notes: The author was supported in part by a grant from the Ministry of Science of Slovenia
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society