M-isometric Composition Operators On Discrete Spaces

TL;DR

This paper studies composition operators on discrete spaces, classifies their underlying graphs, characterizes m-isometries for graphs with one cycle, and solves the Cauchy dual subnormality problem for these operators.

Contribution

It provides a classification of graphs for composition operators, characterizes m-isometries on graphs with one cycle, and addresses the Cauchy dual subnormality problem.

Findings

Classification of underlying graphs of composition operators.

Characterization of m-isometries on graphs with one cycle.

Solution to the Cauchy dual subnormality problem for these operators.

Abstract

In this paper we investigate composition operators on discrete spaces. We establish the classification of underlying graphs of such operators. For one class of such graphs, namely graphs with one cycle, we obtain a characterization of m-isometries. The paper also contains the solution to the Cauchy dual subnormality problem for composition operators on graphs with one cycle.