JORDAN DERIVATIONS AND JORDAN LEFT DERIVATIONS OF BANACH ALGEBRAS

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 2002 English Publisher:The Korean Mathematical SocietyJournal:Communications of the Korean Mathematical Society, volume 17, pages 245-252 (issn: 1225-1763,

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Authors: Park, Kyoo-Hong; Jung, Yong-Soo;

doi: 10.4134/ckms.2002.17.2.245

JORDAN DERIVATIONS AND JORDAN LEFT DERIVATIONS OF BANACH ALGEBRAS

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Abstract

Summary: 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 \(d(A)\subseteq\text{rad}(A)\).

Keywords

Nonassociative topological algebras, Jordan derivation, Jordan left derivation, Banach algebra, Commutators, derivations, elementary operators, etc., Jacobson radical

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