On polynomially hypo-EP operators

TL;DR

This paper introduces polynomially hypo-EP operators, extending existing classes, and explores their properties, characterizations, and matrix representations, providing new insights into their structure and relationships with other operator classes.

Contribution

It presents a new class of polynomially hypo-EP operators, extending hypo-EP and polynomially EP, with detailed properties, characterizations, and matrix representations.

Findings

Characterization of polynomially hypo-EP operators

New operator matrix representations

Connections with existing EP operator classes

Abstract

The purpose of this paper is to present a new class of operators known as polynomially hypo-EP operators, extending the notation of hypo-EP, $n$-hypo-EP, and polynomially EP. The paper explores numerous properties and characterizations of polynomially hypo-EP operators and polynomially EP operators. In addition, we characterize polynomially hypo-EP operators applying the adequate operator matrix representations. By employing these findings, we derive new characterizations of EP, hypo-EP, $n$-EP and $n$-hypo-EP.