Weak-local triple derivations on C*-algebras and JB*-triples
M.J. Burgos, J.C. Cabello, A.M. Peralta

TL;DR
This paper proves that every weak-local triple derivation on JB*-triples is actually a continuous triple derivation, establishing a significant structural property of these maps.
Contribution
It demonstrates that weak-local triple derivations on JB*-triples are necessarily continuous triple derivations, extending understanding of their structure.
Findings
Weak-local triple derivations are continuous triple derivations.
The result applies to JB*-triples, a broad class of Jordan Banach structures.
The proof confirms the structural rigidity of weak-local derivations.
Abstract
We prove that every weak-local triple derivation on a JB-triple (i.e. a linear map such that for each and each , there exists a triple derivation , depending on and , such that ) is a (continuous) triple derivation.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Operator Algebra Research · Algebraic structures and combinatorial models
