Mappings preserving zero products
Let : M! N be a zero-product preserving linear map between algebras. We show that under some mild conditions is a product of a central element and an algebra homomorphism. Our result applies to matrix algebras, standard operator algebras, C -algebras and W -algebras. 1. Introduction. Let M and N be algebras over a eld F and : M! N a linear map. We say that is a zero-product preserving map if (a) (b) = 0 in N whenever ab = 0 in M. For example, if h is an element in the center of N and ' : M ! N is an algebra homomorphism then = h' is zero- product preserving. In this paper, we show that in many interesting cases