Characterization of closed n-paranormal and \(n^{*}\)-paranormal operators

We give several basic and spectral properties of classes of closed n-paranormal and closed \(n^{*}\) $n^{\ast }$ -paranormal operators on dense domains in complex separable Hilbert spaces. We prove that for both of these classes of operators, the null space of \((T-\mu I)\) $(T-\mu I)$ and the range of \(R(E_{\mu })\) $R(E_{\mu })$ are identical, where \(E_{\mu }\) $E_{\mu }$ is the Riesz projection with respect to an isolated point \(\mu \) $\mu$ of the spectrum. We show that they satisfy Weyl’s theorem. Certain properties related to the reduced minimum modulus are also established.