Mappings preserving zero products
Volume 155 / 2003
Studia Mathematica 155 (2003), 77-94
MSC: 08A35, 46L40, 47B48.
DOI: 10.4064/sm155-1-6
Abstract
Let $\theta : {{\cal M}}\to {{\cal N}}$ be a zero-product preserving linear map between algebras. We show that under some mild conditions $\theta $ 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.
