Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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LOCAL SPECTRAL PROPERTIES OF QUASI-DECOMPOSABLE OPERATORS

  • Yoo, Jong-Kwang (Department of Liberal Arts and Science Chodang University) ;
  • Oh, Heung Joon (Department of Liberal Arts and Science Chodang University)
  • Received : 2016.05.11
  • Accepted : 2016.10.14
  • Published : 2016.11.15
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Abstract

In this paper we investigate the local spectral properties of quasidecomposable operators. We show that if $T{\in}L(X)$ is quasi-decomposable, then T has the weak-SDP and ${\sigma}_{loc}(T)={\sigma}(T)$. Also, we show that the quasi-decomposability is preserved under commuting quasi-nilpotent perturbations. Moreover, we show that if $f:U{\rightarrow}{\mathbb{C}}$ is an analytic and injective on an open neighborhood U of ${\sigma}(T)$, then $T{\in}L(X)$ is quasi-decomposable if and only if f(T) is quasi-decomposable. Finally, if $T{\in}L(X)$ and $S{\in}L(Y)$ are asymptotically similar, then T is quasi-decomposable if and only if S does.

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References

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