Suppose that T ri(A, M, B) is a unital triangular algebra, where M is a faithful (A, B)-bimodule, and U is a unital algebra. Let θ : T ri(A, M, B) → U be a bijective zero product preserving additive map. We show that under some mild conditions θ is a product of a central invertible element and a ring isomorphism. Our result applies to block upper triangular matrix algebras, nest algebras on Banach spaces and nest subalgebras of von Neumann algebras.
