Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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STRUCTURAL AND SPECTRAL PROPERTIES OF k-QUASI-*-PARANORMAL OPERATORS

  • ZUO, FEI (College of Mathematics and Information Science Henan Normal University) ;
  • ZUO, HONGLIANG (College of Mathematics and Information Science Henan Normal University)
  • Received : 2014.11.11
  • Accepted : 2015.06.02
  • Published : 2015.06.30
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Abstract

For a positive integer k, an operator T is said to be k-quasi-*-paranormal if ${\parallel}T^{k+2}x{\parallel}{\parallel}T^kx{\parallel}{\geq}{\parallel}T^*T^kx{\parallel}^2$ for all x $\in$ H, which is a generalization of *-paranormal operator. In this paper, we give a necessary and sufficient condition for T to be a k-quasi-*-paranormal operator. We also prove that the spectrum is continuous on the class of all k-quasi-*-paranormal operators.

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References

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