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 ∗ -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 - μ I) and the range of R (E μ) are identical, where E μ is the Riesz projection with respect to an isolated point μ of the spectrum. We show that they satisfy Weyl's theorem. Certain properties related to the reduced minimum modulus are also established. [ABSTRACT FROM AUTHOR]