A result concerning derivations in Banach algebras

Vukman, J.

doi:10.1090/S0002-9939-1992-1079710-7

A result concerning derivations in Banach algebras
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by J. Vukman PDF

Proc. Amer. Math. Soc. 116 (1992), 971-975 Request permission

Abstract:

The main result: Let $A$ be a Banach algebra over the complex field $C$. Suppose there exists a continuous derivation $D:A \to A$, such that $\alpha {D^3} + {D^2}$ is a derivation for some $\alpha \in C$. In this case $D$ maps $A$ into its radical.

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