Self joinings of rigid rank one transformations arise as strong operator topology limits of convex combinations of powers

2019/01/24 by Jon Chaika, Chaika, Jon
Mathematics · #Advanced Topics in Algebra #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1901.08695

openalex publication_date 2019/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is a straightforward generalization Section 2 of arXiv:1805.11167. It shows that for a residual set of transformations in the space of measure preserving transformations, with the weak topology, any self-joining defines a Markov operator that is a strong operator topology limit of convex combinations of powers of the unitary operator given by the transformation.

Related

• Spectral properties and approximations of joinings for infinite rank-one actions
• Disjointness between bounded rank-one transformations
• Bounded rank-one transformations
• Minimal Self-Joinings, Bounded Constructions, and Weak Closure of Ergodic Actions
• A rank one mild mixing system without minimal self joinings