Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON n-*-PARANORMAL OPERATORS

  • Rashid, Mohammad H.M. (Department of Mathematics Faculty of Science P.O. Box(7) Mu'tah University)
  • Received : 2015.10.27
  • Published : 2016.07.31
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Abstract

A Hilbert space operator $T{\in}{\mathfrak{B}}(\mathfrak{H})$ is said to be n-*-paranormal, $T{\in}C(n)$ for short, if ${\parallel}T^*x{\parallel}^n{\leq}{\parallel}T^nx{\parallel}\;{\parallel}x{\parallel}^{n-1}$ for all $x{\in}{\mathfrak{H}}$. 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.

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