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Local Triple Derivations on Real C\(^*\)-Algebras and JB\(^*\)-Triples

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Abstract

We study when a local triple derivation on a real JB\(^*\)-triple is a triple derivation. We find an example of a (real linear) local triple derivation on a rank-one Cartan factor of type I which is not a triple derivation. On the other hand, we find sufficient conditions on a real JB\(^*\)-triple E to guarantee that every local triple derivation on E is a triple derivation.

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Acknowledgments

Authors partially supported by the Spanish Ministry of Economy and Competitiveness, D.G.I. Project No. MTM2014-58984-P, and Junta de Andalucía Grant FQM375.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    Francisco J. Fernández-Polo, Alexis Molino & Antonio M. Peralta

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  1. Francisco J. Fernández-Polo
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  2. Alexis Molino
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  3. Antonio M. Peralta
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Correspondence to Antonio M. Peralta.

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Communicated by Mohammad Sal Mosleihan.

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Fernández-Polo, F.J., Molino, A. & Peralta, A.M. Local Triple Derivations on Real C\(^*\)-Algebras and JB\(^*\)-Triples. Bull. Malays. Math. Sci. Soc. 39, 941–955 (2016). https://doi.org/10.1007/s40840-015-0203-4

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  • DOI: https://doi.org/10.1007/s40840-015-0203-4

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