2-LOCAL DERIVATIONS ON C ∗-ALGEBRAS

. In this paper, we prove that every 2-local derivation on several classes of C*-algebras, such as unital properly infinite, type I or residually finite-dimensional C*-algebras, is a derivation. We show that the following statements are equivalent: (1) every 2-local derivation on a C*-algebra is a derivation, (2) every 2-local derivation on a unital primitive antiliminal and no properly infinite C*-algebra is a derivation. We also show that every 2-local derivation on a group C*-algebra C*(F) or a unital simple infinite-dimensional quasidiagonal C*-algebra, which is stable finite antiliminal C*-algebra, is a derivation.