A note on derivations of Banach algebras
Bull. Korean Math. Soc. 1995 Vol. 32, No. 2, 367-372
Gwang Hui Kim
University of Kangnam
Abstract : Let $A$ be a (complex) Banach algebra. The object of this paper shall be
remove the continuity of derivation in the recently theorems. We prove
that every derivation $D$ on $A$ satisfying $[D(a), a] \in \text{Prad}
(A)$ for all $a \in A$ maps into the radical of $A$. Also if $\alpha
D^3 + D^2$ is a derivation for some $\alpha \in C$ and all minimal
prime ideals are closed, then $D$ maps into its radical.
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