Composition Operators on the Little Lipschitz space of a rooted tree

2024/10/09 by Flavia Colonna, Colonna, Flavia, Rubén A. Martı́nez-Avendaño +1 · 1 citation
Mathematics · #05C05 #05C63 #47A16 #47B37 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2410.14714

openalex publication_date 2024/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we study the composition operators on the little Lipschitz space \mathcal L₀ of a rooted tree T, defined as the subspace of the Lipschitz space \mathcal L consisting of the complex-valued functions f on T such that lim_|v|→∞|f(v)-f(v^-)|=0, where v^- is the vertex adjacent to the vertex v in the path from the root to v and |v| denotes the number of edges from the root to v. Specifically, we give a complete characterization of the self-maps ϕ of T for which the composition operator C_ϕ is bounded and we estimate its operator norm. In addition, we study the spectrum of C_ϕ and the hypercyclicity of the operators λC_ϕ for λ∈ \mathbb C.

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• Frequently hypercyclic composition operators on the little Lipschitz space of a rooted tree

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