Lifting endomorphisms to automorphisms
Operator Algebras
2011-10-26 v2 Functional Analysis
Abstract
Normal endomorphisms of von Neumann algebras need not be extendable to automorphisms of a larger von Neumann algebra, but they always have asymptotic lifts. We describe the structure of endomorphisms and their asymptotic lifts in some detail, and apply those results to complete the identification of asymptotic lifts of unital completely positive linear maps on von Neumann algebras in terms of their minimal dilations to endomorphisms.
Cite
@article{arxiv.math/0703115,
title = {Lifting endomorphisms to automorphisms},
author = {William Arveson and Dennis Courtney},
journal= {arXiv preprint arXiv:math/0703115},
year = {2011}
}
Comments
7 pages, minor clarification of the introduction, new reference