Maps on noncommutative Orlicz spaces

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.

24 pages. Changes in this revised version concerns Section 3

References in corpus (1)

• Composition Operators on Haagerup $L^p$-spaces

Cited by in corpus (6)

• On quantum statistical mechanics; A study guide
• Multiplication operators on non-commutative spaces
• Multipliers on Noncommutative Orlicz Spaces
• On Entropy for general quantum systems
• Noncommutative Orlicz spaces over W*-algebras
• Kadec-Klee property for convergence in measure of noncommutative Orlicz spaces