Maps on noncommutative Orlicz spaces

TL;DR

This paper extends the Pistone-Sempi argument to noncommutative Orlicz spaces, exploring how positive maps on von Neumann algebras induce operators on these spaces, thus aiding the analysis of noncommutative dynamical systems.

Contribution

It characterizes Jordan *-morphisms that induce quantum composition operators on noncommutative Orlicz spaces, expanding the framework's applicability.

Findings

Describes conditions for Jordan *-morphisms to induce quantum composition operators.

Shows noncommutative Orlicz spaces are suitable for analyzing noncommutative dynamical systems.

Extends Pistone-Sempi argument to a noncommutative setting.

Abstract

A generalization of the Pistone-Sempi argument, demonstrating the utility of non-commutative Orlicz spaces, is presented. The question of lifting positive maps defined on von Neumann algebra to maps on corresponding noncommutative Orlicz spaces is discussed. In particular, we describe those Jordan *-morphisms on semifinite von Neumann algebras which in a canonical way induce quantum composition operators on noncommutative Orlicz spaces. Consequently, it is proved that the framework of noncommutative Orlicz spaces is well suited for an analysis of large class of interesting noncommutative dynamical systems.