Jordan Derivations on Prime Rings and Their Applications in Banach Algebras,~I
Commun. Korean Math. Soc. 2013 Vol. 28, No. 3, 535-558
Printed July 1, 2013
Byung-Do Kim
Gangneung-Wonju National University
Abstract : The purpose of this paper is to prove that the noncommutative version of the Singer-Wermer Conjecture is affirmative under certain conditions. Let $A$ be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation $D:A\to A$ such that $D(x)^3[D(x),x]\in \mbox{rad}(A)$ for all $x\in A.$ In this case, we show that $D(A)\subseteq \mbox{rad}(A).$
Keywords : prime and semiprime ring, (Jacobson) radical, Jordan derivation
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