Weak-local triple derivations on C*-algebras and JB*-triples

M. J. Burgos; J. C. Cabello; A. M. Peralta

Weak-local triple derivations on C-algebras and JB-triples

Operator Algebras 2016-04-18 v1

Authors: M. J. Burgos , J. C. Cabello , A. M. Peralta

Abstract

We prove that every weak-local triple derivation on a JB $^*$ -triple $E$ (i.e. a linear map $T: E\to E$ such that for each $\phi \in E^*$ and each $a\in E$ , there exists a triple derivation $\delta_{a,\phi} : E\to E$ , depending on $\phi$ and $a$ , such that $\phi T(a) = \phi \delta_{a,\phi} (a)$ ) is a (continuous) triple derivation.

Keywords

weak-local triple derivation jb*-triple c*-algebra triple derivation linear map

Cite

@article{arxiv.1604.04417,
  title  = {Weak-local triple derivations on C*-algebras and JB*-triples},
  author = {M. J. Burgos and J. C. Cabello and A. M. Peralta},
  journal= {arXiv preprint arXiv:1604.04417},
  year   = {2016}
}

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