Abstract
We prove that, for a complex Hilbert space H with dimension bigger or equal than three, every linear mapping satisfying the 3-local property is a *-monomorphism, that is, every linear mapping satisfying that for every a in B(H) and every in H, there exists a *-automorphism , depending on a, , and , such that
T(a)(xi) = pi(a,xi,eta)(a)(xi), and T(a)(eta) = pi(a,xi,eta)(a)(eta),
is a *-monomorphism. This solves a question posed by Molnar in (Arch Math 102:83-89 2014).