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.