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arXiv · 1303.4569

Local triple derivations on C*-algebras and JB*-triples

María Burgos·Francisco J. Fernández-Polo·Antonio M. Peralta
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Abstract

In a first result we prove that every continuous local triple derivation on a JB$^*$-triple is a triple derivation. We also give an automatic continuity result, that is, we show that local triple derivations on a JB$^*$-triple are continuous even if not assumed a priori to be so. In particular every local triple derivation on a C$^*$-algebra is a triple derivation. We also explore the connections between (bounded local) triple derivations and generalised (Jordan) derivations on a C$^*$-algebra.

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María Burgos, Francisco J. Fernández-Polo, Antonio M. Peralta. 2013-03-22. Local triple derivations on C*-algebras and JB*-triples. https://doi.org/10.1112/blms%2Fbdu024

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