Characterizing homomorphisms and derivations on C*-algebras

The main theorem states that a bounded linear operator h from a unital C^-algebra A into a unital Banach algebra B must be a homomorphism provided that h (1) =1 and the following condition holds: if x, y, z A are such that xy=yz=0, then h (x) h (y) h (z) =0. This theorem covers various known results; in particular it yields Johnson's theorem on local derivations.