Isometries on non-commutative (quantum) Lorentz spaces associated with semi-finite von Neumann algebras

Abstract

In this article we characterize the extreme points of the unit ball of a non-commutative (quantum) Lorentz space associated with a semi-finite von Neumann algebra. This enables us to show that surjective isometries between non-commutative Lorentz spaces are projection disjointness preserving and finiteness preserving, which facilitates a characterization of the structure of these isometries.