Composition operators on Hardy spaces of the homogenous rooted trees

2020/04/07 by Perumal Muthukumar, Muthukumar, Perumal, Saminathan Ponnusamy +1
Mathematics · #37E25 #46B50 #47B33 #47B38 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Primary: 05C05 #Secondary: 30H10

paper · pdf · doi:10.48550/arxiv.2004.03171

openalex publication_date 2020/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Related

• Composition operators on the discrete analogue of generalized Hardy\n space on homogenous trees
• Weighted composition operators between weighted Hardy spaces on rooted trees
• Multiplication operators between discrete Hardy spaces on rooted trees
• Composition operators on generalized Hardy spaces
• Composition Operators on the Little Lipschitz space of a rooted tree