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Continuity of Generalized Jordan Derivations on Semisimple Banach Algebras

  • Mohammad Gholampour
  • Shirin Hejazian
Article

Abstract

A generalized Jordan derivation D on a Banach algebra \({\mathcal {A}}\) is a linear mapping \(D:{\mathcal {A}}\rightarrow {\mathcal {A}}\) for which there exists a positive \(\varepsilon \) satisfying
$$\begin{aligned}\Vert D(a\circ b)-a\circ D(b)-D(a)\circ b\Vert \le \varepsilon \Vert a\Vert \Vert b\Vert \;\;(a, b \in {\mathcal {A}}),\end{aligned}$$
where \(\circ \) denotes the Jordan product on \({\mathcal {A}}\). We study generalized Jordan derivations on Banach algebras and prove that every generalized Jordan derivation on a semisimple Banach algebra is automatically continuous.

Keywords

Generalized homomorphism Jordan derivation Generalized Jordan derivation Automatic continuity 

Mathematics Subject Classification

46H40 47B47 

Notes

Acknowledgements

The authors thank the referees for their careful reading of the article and suggesting valuable comments that improved the quality of this work.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2018

Authors and Affiliations

  1. 1.Department of Pure MathematicsFerdowsi University of MashhadMashhadIran

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