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Bull. Korean Math. Soc. 2001; 38(4): 709-718

Printed December 1, 2001

Copyright © The Korean Mathematical Society.

Derivations on prime rings and Banach algebras

Kil-Woung Jun and Hark-Mahn Kim

Chungnam National University, Chungnam National University

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In this paper we show that if $D$ and $G$ are continuous linear Jordan derivations on a Banach algebra $A$ satisfying $[D(x),x]x - x[G(x),x] \in \text{\rm rad}(A)$ for all $x \in A$, then both $D$ and $G$ map $A$ into $\text{\rm rad}(A).$

Keywords: Jordan derivation, Jacobson radical

MSC numbers: 47B47, 46H99

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