Automatic continuity of derivations onC⁎-algebras andJB⁎-triples

• DOI: 10.1016/j.jalgebra.2013.10.017
• Publication Date: 2013-11-22T22:46:31Z
• Authors: Antonio M. Peralta; Bernard Russo
• Keywords: General Mathematics; Jordan algebra; Mathematics - Operator Algebras; JB*-triple; Pure Mathematics; 01 natural sciences; C*-algebra; Jordan derivation; JB*-algebra; Jordan triple module; FOS: Mathematics; Triple derivation; Derivation; 46L70 17C65; 0101 mathematics; Jordan triple; Operator Algebras (math.OA); Automatic continuity

We introduce the notion of Banach Jordan triple modules and determine precise conditions under which every derivation from a JB⁎-triple E into (Jordan) E-module is continuous. In particular, real or complex its dual space automatically continuous, motivating study (which we have carried out elsewhere) weakly amenable JB⁎-triples. Specializing to C⁎-algebras leads unified treatment derivations modules, shedding light on celebrated theorem Barry Johnson.