|
|||||
|
|
Weak-local derivations and homomorphisms on C*-algebras |
|
| Authors: | Ahlem Ben Ali Essaleh María Isabel Ramírez |
| Institution: | 1. Faculte des Sciences de Monastir, Département de Mathématiques, University of Monastir, Monastir, Tunisia.;2. Departamento de Matemáticas, Universidad de Almería, Almería, Spain. |
| Abstract: | We prove that every weak-local derivation on a C*-algebra is continuous, and the same conclusion remains valid for weak*-local derivations on von Neumann algebras. We further show that weak-local derivations on C*-algebras and weak*-local derivations on von Neumann algebras are derivations. We also study the connections between bilocal derivations and bilocal*-automorphism with our notions of extreme-strong-local derivations and automorphisms. |
| Keywords: | weak-local derivation weak *-local derivation weak-local *-automorphism weak *-local *-automorphism extreme-weak*-local derivation extreme-weak*-local *-automorphism |