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arXiv · 2004.03171

Composition operators on Hardy spaces of the homogenous rooted trees

Perumal Muthukumar·Saminathan Ponnusamy
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Abstract

In \cite{CO-Tp-spaces}, the present authors initiated the study of composition operators on discrete analogue of generalized Hardy space $\mathbb{T}_{p}$ defined on a homogeneous rooted tree. In this article, we give equivalent conditions for the composition operator $C_\phi$ to be bounded on $\mathbb{T}_{p}$ and on $\mathbb{T}_{p,0}$ spaces and compute their operator norm. We also characterize invertible composition operators as well as isometric composition operators on $\mathbb{T}_{p}$ and on $\mathbb{T}_{p,0}$ spaces. Also, we discuss the compactness of $C_\phi$ on $\mathbb{T}_{p}$ and finally prove there are no compact composition operators on $\mathbb{T}_{p,0}$ spaces.

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Perumal Muthukumar, Saminathan Ponnusamy. 2020-04-07. Composition operators on Hardy spaces of the homogenous rooted trees. https://arxiv.org/abs/2004.03171

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