On left derivations and derivations of Banach algebras
Bull. Korean Math. Soc. 1998 Vol. 35, No. 4, 659-665
Abstract : In this paper we show that every left derivation on a semiprime Banach algebra $A$ is a derivation which maps $A$ into the intersection of the center of $A$ and the Jacobson radical of $A$, and hence every left derivation on a semisimple Banach algebra is always zero.
Keywords : derivation, left derivation, Jacobson radical, prime radical, semiprime, semisimple