Weak-local derivations and homomorphisms on C*-algebras
  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. 
Ahlem Ben Ali Essaleh, Antonio M. Peralta, Mar\'ia Isabel Ram\'irez
math.OA math.FA