Local Triple Derivations on C*-Algebras^†

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 derivation
• Generalised Jordan derivation
• Local triple derivation
• Triple derivation
• Unital C*-algebra

2010 Mathematics Subject Classification:

• Primary: 47B47, 46L57
• Secondary: 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.