Local triple derivations on C*-algebras and JB*-triples

Abstract

In a first result we prove that every continuous local triple derivation on a JB${}^{\ast }$-triple is a triple derivation. We also give an automatic continuity result, that is, we show that local triple derivations on a JB${}^{\ast }$-triple are continuous even if not assumed a priori to be so. In particular every local triple derivation on a C${}^{\ast }$-algebra is a triple derivation. We also explore the connections between (bounded local) triple derivations and generalised (Jordan) derivations on a C${}^{\ast }$-algebra.

References in corpus (3)

• Local Derivations on Jordan Triples
• Automatic continuity of derivations on C*-algebras and JB*-triples
• Local triple derivations on C*-algebras

Cited by in corpus (5)

• Linear maps behaving like derivations or anti-derivations at orthogonal elements on C*-algebras
• Characterizing derivations and anti-derivations on group algebras through orthogonality
• On a generalized Semrl's theorem for weak-2-local derivations on B(H)
• Boundedness of completely additive measures with application to 2-local triple derivations
• Weak-local triple derivations on C*-algebras and JB*-triples