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 On left derivations and derivations of Banach algebras Bull. Korean Math. Soc. 1998 Vol. 35, No. 4, 659-665 Yong-Soo Jung 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 MSC numbers : 46H05, 46H20 Downloads: Full-text PDF