Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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CHARACTERIZATIONS OF (JORDAN) DERIVATIONS ON BANACH ALGEBRAS WITH LOCAL ACTIONS

  • Jiankui Li (School of Mathematics East China University of Science and Technology) ;
  • Shan Li (Department of Mathematics Jiangsu University of Technology) ;
  • Kaijia Luo (School of Mathematics East China University of Science and Technology)
  • Received : 2022.04.30
  • Accepted : 2022.09.23
  • Published : 2023.04.30
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Abstract

Let 𝓐 be a unital Banach *-algebra and 𝓜 be a unital *-𝓐-bimodule. If W is a left separating point of 𝓜, we show that every *-derivable mapping at W is a Jordan derivation, and every *-left derivable mapping at W is a Jordan left derivation under the condition W𝓐 = 𝓐W. Moreover we give a complete description of linear mappings 𝛿 and 𝜏 from 𝓐 into 𝓜 satisfying 𝛿(A)B* + A𝜏(B)* = 0 for any A, B ∈ 𝓐 with AB* = 0 or 𝛿(A)◦B* + A◦𝜏(B)* = 0 for any A, B ∈ 𝓐 with A◦B* = 0, where A◦B = AB + BA is the Jordan product.

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Acknowledgement

This work was financially supported by the National Natural Science Foundation of China (Grant No.11871021). The authors thank the referee for valuable suggestions that improve the presentation of this paper.

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