Derivations mapping into the socle, II

Brešar, Matej

doi:10.1090/S0002-9939-98-03993-8

Derivations mapping into the socle, II
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Proc. Amer. Math. Soc. 126 (1998), 181-187 Request permission

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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