Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Lifting endomorphisms to automorphisms

Author(s): William Arveson; Dennis Courtney
Journal: Proc. Amer. Math. Soc. 136 (2008), 2073-2079.
MSC (2000): Primary 46L55, 46L40
Posted: February 14, 2008
MathSciNet review: 2383513
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Abstract | References | Similar articles | Additional information

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:

1.: W. Arveson, Noncommutative dynamics and -semigroups, Springer Monographs in Mathematics, Springer-Verlag, New York, 2003. MR 1978577 (2004g:46082)
2.: W. Arveson, The asymptotic lift of a completely positive map, J. Funct. Anal. (to appear), 2006. Preprint at arXiv:math.OA/0606541 v5.
3.: W. Arveson and A. Kishimoto, A note on extensions of semigroups of -endomorphisms, Proc. Amer. Math. Soc. 116 (1992), no. 3, 769-774. MR 1098393 (93a:46133)
4.: W. Arveson and E. Størmer, Asymptotic lifts of positive linear maps, 2006. Preprint at arXiv:math.OA/0611401.
5.: E. Størmer. Multiplicative properties of positive maps, Math. Scand. 100 (2007), 184-192. MR 2331197

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