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.

The paper entitled "Extreme point methods in the study of isometries on certain non-commutative spaces" (arXiv identifier: 2007.02324) is a significantly revised, updated and extended version of this article