Composition operators on weighted $L^{p}$ spaces of a tree

TL;DR

This paper investigates the properties of composition operators, such as boundedness and compactness, on weighted L^p spaces defined on trees, providing new insights into their operator theory.

Contribution

It offers a comprehensive analysis of composition operators on weighted L^p spaces of trees, including criteria for boundedness, compactness, and Schatten class membership.

Findings

Characterization of bounded composition operators

Criteria for compactness and Schatten class membership

Extension of operator theory to tree-based L^p spaces

Abstract

In this paper, we study the boundedness, compactness and Schatten class membership of composition operators on the weighted $L^{p}$-space of a tree $L^{p}_{\lambda}(T)$ with $1\leq p <\infty$.