m--isometric composition operators on directed graphs with one circuit

TL;DR

This paper characterizes m-isometric composition operators on directed graphs with one circuit, showing their properties and solving related problems including hyperexpansiveness, completion, and subnormality.

Contribution

It provides a complete characterization of m-isometries on such graphs and addresses several open problems in the theory of composition operators.

Findings

Complete characterization of m-isometries on directed graphs with one circuit

Hyperexpansiveness coincides with 2-isometricity in this class

Solution to the Cauchy dual subnormality problem for graphs with a single circuit

Abstract

The aim of this paper is to investigate $m$--isometric composition operators on directed graphs with one circuit. We establish a characterization of $m$--isometries and prove that complete hyperexpansiveness coincides with $2$--isometricity within this class. We discuss the $m$--isometric completion problem for unilateral weighted shifts and for composition operators on directed graphs with one circuit. The paper is concluded with an affirmative solution of the Cauchy dual subnormality problem in the subclass with circuit containing one element.