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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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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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
Keywords
- Triple derivation
- Local triple derivation (continuous)
- Symmetrized triple product
- C\(^*\)-algebra
- Real C\(^*\)-algebra
- JB\(^*\)-triple
- Real JB\(^*\)-triple