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Jordan, Jordan Right and Jordan Left Derivations on Convolution Algebras

  • Mohammad Hossein Ahmadi Gandomani
  • Mohammad Javad Mehdipour
Original Paper
  • 5 Downloads

Abstract

In this paper, we investigate Jordan derivations, Jordan right derivations and Jordan left derivations of \(L_0^\infty ({{\mathcal {G}}})^*\). We show that any Jordan (right) derivation on \(L_0^\infty ({{\mathcal {G}}})^*\) is a (right) derivation on \(L_0^\infty ({{\mathcal {G}}})^*\) and the zero map is the only Jordan left derivation on \(L_0^\infty ({{\mathcal {G}}})^*\). Then, we prove that the range of a Jordan (right) derivation on \(L_0^\infty ({{\mathcal {G}}})^*\) is contained into \(\hbox {rad}(L_0^\infty ({{\mathcal {G}}})^*)\). Finally, we establish that the product of two Jordan (right) derivations of \(L_0^\infty ({{\mathcal {G}}})^*\) is always a derivation on \(L_0^\infty ({{\mathcal {G}}})^*\) and there is no nonzero centralizing Jordan (right) derivation on \(L_0^\infty ({{\mathcal {G}}})^*\).

Keywords

Locally compact group Jordan derivation Jordan right derivation Jordan left derivation k-centralizing mapping 

Mathematics Subject Classification

Primary 43A15 Secondary 47B47 16W25 

Notes

Acknowledgements

The authors would like to thank the referee for his/her helpful comments and suggestions.

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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  • Mohammad Hossein Ahmadi Gandomani
    • 1
  • Mohammad Javad Mehdipour
    • 1
  1. 1.Department of MathematicsShiraz University of TechnologyShirazIran

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