Lifting endomorphisms to automorphisms
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- by William Arveson and Dennis Courtney PDF
- Proc. Amer. Math. Soc. 136 (2008), 2073-2079 Request permission
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.References
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Additional Information
- William Arveson
- Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
- Email: arveson@math.berkeley.edu
- Dennis Courtney
- Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
- Email: djc@math.berkeley.edu
- Received by editor(s): March 5, 2007
- Published electronically: February 14, 2008
- Communicated by: Marius Junge
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2073-2079
- MSC (2000): Primary 46L55, 46L40
- DOI: https://doi.org/10.1090/S0002-9939-08-09186-7
- MathSciNet review: 2383513