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arXiv · 1208.0096

Automatic continuity of derivations on C*-algebras and JB*-triples

Antonio M. Peralta·Bernard Russo
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Abstract

We introduce the notion of a Jordan triple module and determine the precise conditions under which every derivation from a JB*-triple E into a Banach (Jordan) triple E-module is continuous. In particular, every derivation from a real or complex JB*-triple into its dual space is automatically continuous. Among the consequences, we prove that every triple derivation from a C*-algebra A to a Banach triple A-module is continuous. In particular, every Jordan derivation from A to a Banach A-bimodule is a derivation, a result which complements a classical theorem due to B.E. Johnson and solves a problem which has remained open for over ten years.

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Antonio M. Peralta, Bernard Russo. 2012-08-01. Automatic continuity of derivations on C*-algebras and JB*-triples. https://arxiv.org/abs/1208.0096

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