Characterizations of closed EP operators on Hilbert spaces

TL;DR

This paper characterizes closed and bounded EP operators on Hilbert spaces and establishes a relationship between the reduced minimum modulus and spectral radius for bounded EP operators.

Contribution

It provides new characterizations of closed EP operators and proves an inequality relating spectral properties of bounded EP operators.

Findings

Characterizations of closed EP operators on Hilbert spaces

Inequality $ ext{gamma}(T) \\leq r(T)$ for bounded EP operators

Insights into spectral properties of EP operators

Abstract

In this paper, we present intriguing findings that characterize both the closed (unbounded) and bounded EP operators on Hilbert spaces. Additionally, we demonstrate the result $\gamma(T) \leq r(T)$, where $T$ is a bounded EP operator, and $\gamma(T) \text{ and } r(T)$ represent the reduced minimum modulus and the spectral radius of $T$, respectively.