Asymptotic lifts of positive linear maps
Copyright policy )Asymptotic lifts of positive linear maps
We show that the notion of asymptotic lift generalizes naturally to normal positive maps $ϕ$ 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 of M, and characterize when that subsystem is a Jordan subalgebra of M in terms of the asymptotic multiplicative properties of $ϕ$.
13 pages
- University of California, Berkeley United States
- University of Oslo Norway
ergodic theory, von Neumann algebras, General theory of von Neumann algebras, Mathematics - Operator Algebras, Functional Analysis (math.FA), Mathematics - Functional Analysis, positive maps, FOS: Mathematics, asymptotic lifts, Noncommutative dynamical systems, Operator Algebras (math.OA), Automorphisms of selfadjoint operator algebras
ergodic theory, von Neumann algebras, General theory of von Neumann algebras, Mathematics - Operator Algebras, Functional Analysis (math.FA), Mathematics - Functional Analysis, positive maps, FOS: Mathematics, asymptotic lifts, Noncommutative dynamical systems, Operator Algebras (math.OA), Automorphisms of selfadjoint operator algebras
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