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 $D(A)\subseteq \mbox{rad}(A).$
Keywords : semiprime ring, Jordan derivation
MSC numbers : 16N60, 16W25, 17B40
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