Local Derivations on Jordan Triples

TL;DR

This paper extends Kadison's concept of local derivations from von Neumann algebras to Jordan triples, proving that continuous local derivations in this setting are also derivations.

Contribution

It establishes an analogous result for Jordan triples, showing that continuous local derivations are derivations, thus generalizing Kadison's theorem.

Findings

Continuous local derivations on Jordan triples are derivations.

Generalization of Kadison's theorem to Jordan triples.

Provides foundational results for the structure of Jordan triples.

Abstract

R.V. Kadison defined the notion of local derivation on an algebra and proved that every continuous local derivation on a von Neumann algebra is a derivation (Kadison 1990). We provide the analogous result in the setting of Jordan triples.