ON n-*-PARANORMAL OPERATORS

Title & Authors
ON n-*-PARANORMAL OPERATORS

Abstract
A Hilbert space operator $\small{T{\in}{\mathfrak{B}}(\mathfrak{H})}$ is said to be n-*-paranormal, $\small{T{\in}C(n)}$ for short, if $\small{{\parallel}T^*x{\parallel}^n{\leq}{\parallel}T^nx{\parallel}\;{\parallel}x{\parallel}^{n-1}}$ for all $\small{x{\in}{\mathfrak{H}}}$. 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.
Keywords
*-paranormal operators;n-*-paranormal operators;finite operators;Fuglede-Putnam theorem;Weyl theorem;
Language
English
Cited by
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