# Maps on noncommutative Orlicz spaces

@article{Labuschagne2009MapsON, title={Maps on noncommutative Orlicz spaces}, author={Louis E. Labuschagne and Wladyslaw A. Majewski}, journal={arXiv: Operator Algebras}, year={2009} }

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…

## 20 Citations

Noncommutative Orlicz spaces over W*-algebras

- Mathematics
- 2014

Using the Falcone--Takesaki theory of noncommutative integration, we construct a family of noncommutative Orlicz spaces that are canonically associated to an arbitrary W*-algebra without any choice…

A crossed product approach to Orlicz spaces

- Mathematics
- 2013

We show how the known theory of noncommutative Orlicz spaces for semifinite von Neumann algebras equipped with an fns trace, may be recovered using crossed product techniques. Then using this as a…

Multipliers on noncommutative Orlicz spaces

- Mathematics
- 2012

Abstract We establish very general criteria for the existence of multiplication operators between noncommutative Orlicz spaces L ψ0 and Lψ1 . We then show that these criteria contain existing…

Dynamics on Noncommutative Orlicz Spaces

- Mathematics
- 2020

Quantum dynamical maps are defined and studied for quantum statistical physics based on Orlicz spaces. This complements earlier work [26] where we made a strong case for the assertion that…

Weighted Noncommutative Banach Function Spaces

- MathematicsTrends in Mathematics
- 2019

We review the concept of a weighted noncommutative Banach function space. This concept constitutes a generalisation of the by now well-known theory of noncommutative Banach function spaces associated…

Kadec–Klee property for convergence in measure of noncommutative Orlicz spaces

- Mathematics
- 2016

Abstract This paper studies the Kadec–Klee property for convergence in measure of noncommutative Orlicz spaces L φ ( M ˜ , τ ) , where M ˜ is the space of τ -measurable operators, and φ is an Orlicz…

Noncommutative Yosida–Hewitt theorem in noncommutative Calderón–Lozanovskiĭ spaces

- Mathematics
- 2020

Let
$${\mathcal {M}}$$
be a diffuse von Neumann algebra equipped with a fixed faithful, normal, semi-finite trace and let
$$\varphi$$
be an Orlicz function. In this paper, a new approach to the…

On Applications of Orlicz Spaces to Statistical Physics

- Mathematics, Physics
- 2014

We present a new rigorous approach based on Orlicz spaces for the description of the statistics of large regular statistical systems, both classical and quantum. The pair of Orlicz spaces we…

Multiplication operators on non-commutative spaces

- MathematicsJournal of Mathematical Analysis and Applications
- 2019

Abstract Boundedness and compactness properties of multiplication operators on quantum (non-commutative) function spaces are investigated. For endomorphic multiplication operators these properties…

Quantum dynamics on Orlicz spaces

- Physics, Mathematics
- 2016

Quantum dynamical maps are defined and studied for quantum statistical physics based on Orlicz spaces. This complements earlier work [W. A. Majewski, L.E. Labuschagne, Ann. H. Poincare. 15,…

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