Characterizations of closed EP operators on Hilbert spaces

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.