Maps on noncommutative Orlicz spaces
Abstract
A generalization of the PistoneSempi argument, demonstrating the utility of noncommutative 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2009
 arXiv:
 arXiv:0902.3078
 Bibcode:
 2009arXiv0902.3078L
 Keywords:

 Mathematics  Operator Algebras;
 Mathematical Physics;
 46L52;
 47B33
 EPrint:
 24 pages. Changes in this revised version concerns Section 3