LEFT JORDAN DERIVATIONS ON BANACH ALGEBRAS AND RELATED MAPPINGS

Title & Authors
LEFT JORDAN DERIVATIONS ON BANACH ALGEBRAS AND RELATED MAPPINGS
Jung, Yong-Soo; Park, Kyoo-Hong;

Abstract
In this note, we obtain range inclusion results for left Jordan derivations on Banach algebras: (i) Let $\small{\delta}$ be a spectrally bounded left Jordan derivation on a Banach algebra A. Then $\small{\delta}$ maps A into its Jacobson radical. (ii) Let $\small{\delta}$ be a left Jordan derivation on a unital Banach algebra A with the condition sup{r$\small{(c^{-1}\delta(c))}$ : c $\small{\in}$ A invertible} < $\small{\infty}$. Then $\small{\delta}$ 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;
Language
English
Cited by
1.
A characterization of generalized Jordan derivations on Banach algebras, Periodica Mathematica Hungarica, 2014, 69, 2, 139
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