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 M_∞ ⊆ M 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

Authors