Vol. 233, No. 1, 2007

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Asymptotic lifts of positive linear maps

William Arveson and Erling Størmer

Vol. 233 (2007), No. 1, 1–14
Abstract

We show that the notion of asymptotic lift generalizes naturally to normal positive maps ϕ : M M acting on von Neumann algebras M. We focus on cases in which the domain of the asymptotic lift can be embedded as an operator subsystem MM and characterize when M is a Jordan subalgebra of M in terms of the asymptotic multiplicative properties of ϕ.

Keywords

von Neumann algebras, positive maps, ergodic theory, asymptotic lifts

Mathematical Subject Classification

Primary: 46L55

Secondary: 46L40

Milestones

Received: 15 November 2006
Accepted: 9 July 2007

Authors
William Arveson
Department of Mathematics
University of California
Berkeley, CA 94720
United States
http://math.berkeley.edu/~arveson/
Erling Størmer
University of Oslo
P.O. Box 1053
0316 Oslo
Norway