On mappings preserving zero products

Abstract

Let A and B be unital complex algebras, assume that A is a semisimple Banach algebra with non-zero socle. We prove that under certain conditions every bijective linear map T: A → B, which preserves zero products, is an isomorphism multiplied by a central invertible element. Zero Jordan product preservers, and a more restrictive version of zero product preservers are also studied.