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

1997/04/22 by Mascioni, Vania, Molnar, Lajos
#46L10 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.math/9704216

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.

Related

• Linear maps between C*-algebras whose adjoints preserve extreme points\n of the dual ball
• Operational extreme points of unital completely positive maps
• Mankiewicz's theorem and the Mazur--Ulam property for C*-algebras
• Geometric Aspects of C^*-Extreme Points
• Almost preserved extreme points