Lifting endomorphisms to automorphisms

Details Lifting endomorphisms to automorphisms Lifting endomorphisms to automorphisms

2007-03-04

arxiv.org/abs/math/0703115v2

Proc. Amer. Math. Soc. 136 (2008), 2073-2079

Mathematics

Operator Algebras

7 pages, minor clarification of the introduction, new reference

Scientific paper

10.1090/S0002-9939-08-09186-7

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.

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