Local Triple Derivations on<i>C</i>*-Algebras^†

Abstract

Abstract We prove that every bounded local triple derivation on a unital C*-algebra is a triple derivation. A similar statement is established in the category of unital JB*-algebras. Key Words: Generalised derivationGeneralised Jordan derivationLocal triple derivationTriple derivationUnital C*-algebra2010 Mathematics Subject Classification: Primary: 47B47, 46L57Secondary: 17C65, 46L05, 46L08 ACKNOWLEDGMENTS Authors partially supported by the Spanish Ministry of Economy and Competitiveness, D.G.I. project no. MTM2011-23843, and Junta de Andalucía grants FQM0199 and FQM3737. The first author was partially supported by a Grant from the GENIL-YTR program. †To Professor Juan Martinez on the occasion of his retirement. Notes Communicated by A. Elduque.