Strong commutativity preserving maps on von Neumann algebras

Abstract

Let be a von Neumann algebra without central summands of type . Assume that is a surjective map. We prove that if preserves strong commutativity, then for all , where satisfies and is a map from into . Related results concerning strong factor commutativity preserving maps are given.

Keywords:

• strong commutativity
• preserving maps
• von Neumann algebras

AMS Subject Classifications:

• Primary: 16W25
• Secondary: 47B47