Derivations of semiprime rings and noncommutative Banach algebras
Commun. Korean Math. Soc. 2002 Vol. 17, No. 4, 607-618 Printed December 1, 2002
Byung-Do Kim Kangnung National University
Abstract : Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation $D:A\to A$ such that $D(x)[D(x),x]D(x)\in \mbox{rad}(A)$ for all $x\in A.$ In this case, we have $D(A)\subseteq \mbox{rad}(A).$
