Bulletin of the
Korean Mathematical Society BKMS

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