Jordan derivations and Jordan left derivations of Banach algebras
Commun. Korean Math. Soc. 2002 Vol. 17, No. 2, 245-252
Printed June 1, 2002
Kyoo-Hong Park, Yong-Soo Jung
Seowon University, Chungnam National University
Abstract : In this paper we obtain some results concerning Jordan derivations and Jordan left derivations mapping into the Jacobson radical. Our main result is the following: Let $d$ be a Jordan derivation (resp. Jordan left derivation) of a complex Banach algebra $A$. If $d^{2}(x)=0$ for all $x \in A$, then we have $d(A) \subseteq rad(A)$
Keywords : Banach algebra, Jordan derivation, Jordan left derivation, Jacobson radical
MSC numbers : Primary 46H99; Secondary 47B47
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