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Finite Operators and Weyl Type Theorems for Quasi-*-n-Paranormal Operators

  • ZUO, FEI (College of Mathematics and Information Science, Henan Normal University) ;
  • YAN, WEI (College of Mathematics and Information Science, Henan Normal University)
  • Received : 2014.12.15
  • Accepted : 2015.05.13
  • Published : 2015.12.23

Abstract

In this paper, we mainly obtain the following assertions: (1) If T is a quasi-*-n-paranormal operator, then T is finite and simply polaroid. (2) If T or $T^*$ is a quasi-*-n-paranormal operator, then Weyl's theorem holds for f(T), where f is an analytic function on ${\sigma}(T)$ and is not constant on each connected component of the open set U containing ${\sigma}(T)$. (3) If E is the Riesz idempotent for a nonzero isolated point ${\lambda}$ of the spectrum of a quasi-*-n-paranormal operator, then E is self-adjoint and $EH=N(T-{\lambda})=N(T-{\lambda})^*$.

Keywords

References

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