Composition operators on Hardy spaces of the homogenous rooted trees

Authors

Perumal Muthukumar, Indian Statistical Institute Bangalore
Saminathan Ponnusamy, Indian Institute of Technology Madras

Article Type

Research Article

Publication Title

Monatshefte fur Mathematik

Abstract

In Muthukumar and Ponnusamy (Bull Malays Math Sci Soc 40(4):1801–1815, 2017), the present authors initiated the study of composition operators on discrete analogue of generalized Hardy space Tp defined on a homogeneous rooted tree. In this article, we give equivalent conditions for the composition operator Cϕ to be bounded on Tp and on Tp, spaces and compute their operator norm. We also characterize invertible composition operators as well as isometric composition operators on Tp and on Tp, spaces. Also, we discuss the compactness of Cϕ on Tp and finally prove there are no compact composition operators on Tp, spaces.

First Page

721

Last Page

743

DOI

10.1007/s00605-020-01410-x

Publication Date

7-1-2020

Comments

Open Access, Green

Recommended Citation

Muthukumar, Perumal and Ponnusamy, Saminathan, "Composition operators on Hardy spaces of the homogenous rooted trees" (2020). Journal Articles. 221.
https://digitalcommons.isical.ac.in/journal-articles/221