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Topological transitivity and mixing of composition operators

Research paper by Frédéric Bayart, Udayan B. Darji; Benito Pires

Indexed on: 04 Jun '18Published on: 31 May '18Published in: Journal of Mathematical Analysis and Applications



Abstract

Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Frédéric Bayart, Udayan B. Darji, Benito Pires Let X = ( X , B , μ ) be a σ-finite measure space and f : X → X be a measurable transformation such that the composition operator T f : φ ↦ φ ∘ f is a bounded linear operator acting on L p ( X , B , μ ) , 1 ≤ p < ∞ . We provide a necessary and sufficient condition on f for T f to be topologically transitive or topologically mixing. We also characterize the topological dynamics of composition operators induced by weighted shifts, non-singular odometers and inner functions. The results provided in this article hold for composition operators acting on more general Banach spaces of functions.