Linear maps on factors which preserve the extreme points of the unit ball

Abstract

The aim of this paper is to characterize those linear maps from a von Neumann factor $\A$ into itself which preserve the extreme points of the unit ball of $\A$. For example, we show that if $\A$ is infinite, then every such linear preserver can be written as a fixed unitary operator times either a unital *-homomorphism or a unital *-antihomomorphism.