[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2010.47.1.151

LEFT JORDAN DERIVATIONS ON BANACH ALGEBRAS AND RELATED MAPPINGS

Jung, Yong-Soo (Department of Mathematics, Sun Moon University)
Park, Kyoo-Hong (Department of Mathematics Education, Seowon University)

Publication Information

Bulletin of the Korean Mathematical Society / v.47, no.1, 2010 , pp. 151-157 More about this Journal

Abstract

In this note, we obtain range inclusion results for left Jordan derivations on Banach algebras: (i) Let $\delta$ be a spectrally bounded left Jordan derivation on a Banach algebra A. Then $\delta$ maps A into its Jacobson radical. (ii) Let $\delta$ be a left Jordan derivation on a unital Banach algebra A with the condition sup{r $(c^{-1}\delta(c))$ : c $\in$ A invertible} < $\infty$ . Then $\delta$ maps A into its Jacobson radical. Moreover, we give an exact answer to the conjecture raised by Ashraf and Ali in [2, p. 260]: every generalized left Jordan derivation on 2-torsion free semiprime rings is a generalized left derivation.

Keywords

(generalized) left Jordan derivation; (generalized) left derivation; derivation; spectral boundedness; Jacobson radica;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)
Times Cited By Web Of Science : 0 (Related Records In Web of Science)
Times Cited By SCOPUS : 1

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