Abstract
A Hilbert space operator <TEX>$T{\in}{\mathfrak{B}}(\mathfrak{H})$</TEX> is said to be n-*-paranormal, <TEX>$T{\in}C(n)$</TEX> for short, if <TEX>${\parallel}T^*x{\parallel}^n{\leq}{\parallel}T^nx{\parallel}\;{\parallel}x{\parallel}^{n-1}$</TEX> for all <TEX>$x{\in}{\mathfrak{H}}$</TEX>. We proved some properties of class C(n) and we proved an asymmetric Putnam-Fuglede theorem for n-*-paranormal. Also, we study some invariants of Weyl type theorems. Moreover, we will prove that a class n-* paranormal operator is finite and it remains invariant under compact perturbation and some orthogonality results will be given.
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