Noncommutative Orlicz spaces over W*-algebras
arXiv:1409.0189
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.
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