On the Dynamics of Weighted Composition Operators

2025/06/04 by Nilson C. Bernardes, Bernardes, Nilson C., A. Bonilla +3 · 1 citation
Mathematics · #46E30 #47B33. Secondary 46E15 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary 47A16

paper · pdf · doi:10.48550/arxiv.2506.04476

openalex publication_date 2025/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the properties of power-boundedness, Li-Yorke chaos, distributional chaos, absolutely Cesàro boundedness and mean Li-Yorke chaos for weighted composition operators on L^p(μ) spaces and on C₀(Ω) spaces. We illustrate the general results by presenting several applications to weighted shifts on the classical sequence spaces c₀(ℕ), c₀(ℤ), ℓ^p(ℕ) and ℓ^p(ℤ) (1 ≤ p < ∞) and to weighted translation operators on the classical function spaces C₀[1,∞), C₀(ℝ), L^p[1,∞) and L^p(ℝ) (1 ≤ p < ∞).

Citations

• Distributional chaos for composition operators on L^p-spaces
• Kitai's Criterion for Composition Operators
• Li-Yorke Chaotic Weighted Composition Operators
• Expansivity and strong structural stability for composition operators on L^p spaces
• Distributional chaos for weighted translation operators on groups
• Cesàro bounded operators in Banach spaces
• Li-Yorke and distributionally chaotic operators

Cited by

• On the Dynamics of Weighted Composition Operators II

Related

• Li-Yorke Chaotic Weighted Composition Operators
• Distributional chaos for composition operators on L^p-spaces
• Dynamics of weighted shifts on ℓ^p-sums and c₀-sums
• Distributional and mean Li-Yorke chaos for weighted shifts on Fréchet sequence spaces
• On the Dynamics of Weighted Composition Operators II