Maps on noncommutative Orlicz spaces

Details Maps on noncommutative Orlicz spaces Maps on noncommutative Orlicz spaces

2009-02-18

arxiv.org/abs/0902.3078v2

Mathematics

Operator Algebras

24 pages. Changes in this revised version concerns Section 3

Scientific paper

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.

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