Extension of m-isometric weighted composition operators on directed graphs

TL;DR

This paper explores the properties of k-quasi-m-isometric and weighted composition operators on directed graphs with complex structures, extending the understanding of their behavior in such graph settings.

Contribution

It introduces the analysis of k-quasi-m-isometric and weighted composition operators specifically on directed graphs with circuits and multiple branching vertices, expanding existing operator theory.

Findings

Characterization of k-quasi-m-isometric operators on directed graphs

Extension of weighted composition operators to complex graph structures

New insights into operator behavior on graphs with circuits and branches

Abstract

In this paper, we discuss k-quasi-m-isometric composition operators and weighted composition operators on directed graphs with one circuit and more than one branching vertex.