Noncommutative Orlicz spaces over W*-algebras
Operator Algebras
2018-07-26 v3 Functional Analysis
Abstract
Using the Falcone--Takesaki theory of noncommutative integration and Kosaki's canonical representation, we construct a family of noncommutative Orlicz spaces that are associated to an arbitrary W*-algebra without any choice of weight involved, and we show that this construction is functorial over the category of W*-algebras with *-isomorphisms as arrows. Under a choice of representation, these spaces are isometrically isomorphic to Kunze's noncommutative Orlicz spaces over crossed products.
Cite
@article{arxiv.1409.0189,
title = {Noncommutative Orlicz spaces over W*-algebras},
author = {Ryszard Paweł Kostecki},
journal= {arXiv preprint arXiv:1409.0189},
year = {2018}
}
Comments
author note: a large overlap of Sections 2 and 3 with some subsections of my own overview text arXiv:1307.4818 stems from the character of these Sections: they provide an introduction to the work of others, and carry no claim of novelty