Characterizations of closed EP operators on Hilbert spaces

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.