Local triple derivations on C*-algebras and JB*-triples
Mar\'ia Burgos, Francisco J. Fern\'andez-Polo, Antonio M. Peralta

TL;DR
This paper proves that all continuous local triple derivations on JB*-triples are actual triple derivations and that such derivations on C*-algebras are automatically continuous, establishing key structural properties.
Contribution
It demonstrates that local triple derivations on JB*-triples are genuine derivations and establishes their automatic continuity, extending to C*-algebras.
Findings
Every continuous local triple derivation on a JB*-triple is a triple derivation.
Local triple derivations on C*-algebras are automatically continuous.
Connections between local triple derivations and generalized Jordan derivations are explored.
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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