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THE SPECTRAL CONTINUITY OF ESSENTIALLY HYPONORMAL OPERATORS

  • Kim, An-Hyun (Department of Mathematics Changwon National University) ;
  • Ryu, Eun-Jin (Department of Mathematics Changwon National University)
  • Received : 2013.11.03
  • Published : 2014.07.31

Abstract

If A is a unital Banach algebra, then the spectrum can be viewed as a function ${\sigma}$ : 𝕬 ${\rightarrow}$ 𝕾, mapping each T ${\in}$ 𝕬 to its spectrum ${\sigma}(T)$, where 𝕾 is the set, equipped with the Hausdorff metric, of all compact subsets of $\mathbb{C}$. This paper is concerned with the continuity of the spectrum ${\sigma}$ via Browder's theorem. It is shown that ${\sigma}$ is continuous when ${\sigma}$ is restricted to the set of essentially hyponormal operators for which Browder's theorem holds, that is, the Weyl spectrum and the Browder spectrum coincide.

Keywords

spectrum;essential spectrum;spectral continuity;Weyl's theorem;Browder's theorem

Acknowledgement

Supported by : Changwon National University

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