Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ON LOCAL SPECTRAL PROPERTIES OF GENERALIZED SCALAR OPERATORS

  • Yoo, Jong-Kwang (Department of Liberal Arts and Science Chodang University) ;
  • Han, Hyuk (Department of Liberal Arts, Kongju National University)
  • Received : 2010.03.03
  • Accepted : 2010.04.23
  • Published : 2010.06.30
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Abstract

In this paper, we prove that if $T{\in}L$(X) is a generalized scalar operator then Ker $T^p$ is the quasi-nilpotent part of T for some positive integer $p{\in}{\mathbb{N}}$. Moreover, we prove that a generalized scalar operator with finite spectrum is algebraic. In particular, a quasi-nilpotent generalized scalar operator is nilpotent.

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References

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