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

Abstract

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