• Title, Summary, Keyword: Jordan derivation

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JORDAN DERIVATIONS AND JORDAN LEFT DERIVATIONS OF BANACH ALGEBRAS

  • Park, Kyoo-Hong;Jung, Yong-Soo
    • Communications of the Korean Mathematical Society
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    • v.17 no.2
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    • pp.245-252
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    • 2002
  • 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) ⊆ red(A)

LEFT JORDAN DERIVATIONS ON BANACH ALGEBRAS AND RELATED MAPPINGS

  • Jung, Yong-Soo;Park, Kyoo-Hong
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.1
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    • pp.151-157
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    • 2010
  • 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.

JORDAN GENERALIZED DERIVATIONS ON TRIVIAL EXTENSION ALGEBRAS

  • Bahmani, Mohammad Ali;Bennis, Driss;Vishki, Hamid Reza Ebrahimi;Attar, Azam Erfanian;Fahid, Barahim
    • Communications of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.721-739
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    • 2018
  • In this paper, we investigate the problem of describing the form of Jordan generalized derivations on trivial extension algebras. One of the main results shows, under some conditions, that every Jordan generalized derivation on a trivial extension algebra is the sum of a generalized derivation and an antiderivation. This result extends the study of Jordan generalized derivations on triangular algebras (see [12]), and also it can be considered as a "generalized" counterpart of the results given on Jordan derivations of a trivial extension algebra (see [11]).