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Dual Space Valued Mappings on C\(^*\)-Algebras Which Are Ternary Derivable at Zero

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Abstract

Extending derivability of a mapping from one point of a \(\mathrm C^*\)-algebra to the entire space is one of the interesting problems in derivation theory. In this paper, by considering a \(\mathrm C^*\)-algebra A as a Jordan triple with triple product \(\{a,b,c\}=(ab^*c+cb^*a)/2\), and its dual space as a ternary A-module, we prove that a continuous conjugate linear mapping T from A into its dual space is a ternary derivation whenever it is ternary derivable at zero and the element T(1) is skew-symmetric.

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Acknowledgements

The authors would like to thank the anonymous referee for the careful review and the helpful suggestions.

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  1. Department of Mathematics, University of Birjand, Birjand, Iran

    Mohsen Niazi & Mohammad Reza Miri

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  1. Mohsen Niazi
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  2. Mohammad Reza Miri
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Correspondence to Mohsen Niazi.

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Niazi, M., Miri, M.R. Dual Space Valued Mappings on C\(^*\)-Algebras Which Are Ternary Derivable at Zero. Mediterr. J. Math. 18, 245 (2021). https://doi.org/10.1007/s00009-021-01910-6

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  • DOI: https://doi.org/10.1007/s00009-021-01910-6

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