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

TL;DR

This paper characterizes the extreme points of non-commutative Lorentz spaces linked to semi-finite von Neumann algebras and uses this to describe the structure of their isometries.

Contribution

It provides a novel characterization of surjective isometries on non-commutative Lorentz spaces, revealing their preservation properties and structural features.

Findings

Surjective isometries are projection disjointness preserving.

Isometries are also finiteness preserving.

Structural characterization of isometries in non-commutative Lorentz spaces.

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.