We introduce and study weak-2-local symmetric maps between C * -algebras A and B as non necessarily linear nor continuous maps ∆ : A → B such that for each a, b ∈ A and φ ∈ B * , there exists a symmetric linear map T a,b,φ : A → B, depending on a, b and φ, satisfying φ∆(a) = φT a,b,φ (a) and φ∆(b) = φT a,b,φ (b). We prove that every weak-2-local symmetric map between C * -algebras is a linear map. Among the consequences we show that every weak-2-local * -derivation on a general C * -algebra is a (linear) * -derivation. We also establish a 2-local version of the Kowalski-S lodkowski theorem for general C *algebras by proving that every 2-local * -homomorphism between C * -algebras is a (linear) * -homomorphism.

No abstract

No abstract

Abstract. We prove that, for every complex Hilbert space H, every weak-2-local derivation on B(H) or on K(H) is a linear derivation. We also establish that every weak-2-local derivation on an atomic von Neumann algebra or on a compact C * -algebra is a linear derivation.

No abstract