Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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CONTINUITY OF THE SPECTRUM ON A CLASS A(κ)

  • Jeon, In Ho (Department of Mathematics Education Seoul National University of Education) ;
  • Kim, In Hyoun (Department of Mathematics University of Incheon)
  • Received : 2013.02.06
  • Accepted : 2013.03.18
  • Published : 2013.03.30
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Abstract

Let T be a bounded linear operator on a complex Hilbert space $\mathfrak{H}$. An operator T is called class A operator if ${\mid}T^2{\mid}{\geq}{\mid}T{\mid}^2$ and is called class $A({\kappa})$ operator if $(T^*{\mid}T{\mid}^{2{\kappa}}T)^{\frac{1}{{\kappa}+1}}{\geq}{\mid}T{\mid}^2$ for a positive number ${\kappa}$. In this paper, we show that ${\sigma}$ is continuous when restricted to the set of class $A({\kappa})$ operators.

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References

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