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Fall 2011 Maps on noncommutative Orlicz spaces
Louis E. Labuschagne, Władysław A. Majewski
Illinois J. Math. 55(3): 1053-1081 (Fall 2011). DOI: 10.1215/ijm/1369841796


A generalization of the Pistone–Sempi argument, demonstrating the utility of noncommutative Orlicz spaces, is presented. In particular, regular quantum statistical systems are described. 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 a large class of interesting noncommutative dynamical systems.


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Louis E. Labuschagne. Władysław A. Majewski. "Maps on noncommutative Orlicz spaces." Illinois J. Math. 55 (3) 1053 - 1081, Fall 2011.


Published: Fall 2011
First available in Project Euclid: 29 May 2013

zbMATH: 1272.46052
MathSciNet: MR3069295
Digital Object Identifier: 10.1215/ijm/1369841796

Primary: 46L52 , 47B33
Secondary: 47L90

Rights: Copyright © 2011 University of Illinois at Urbana-Champaign


Vol.55 • No. 3 • Fall 2011
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