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http://dx.doi.org/10.4134/CKMS.2014.29.3.401

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)
Publication Information
Communications of the Korean Mathematical Society / v.29, no.3, 2014 , pp. 401-408 More about this Journal
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;
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Times Cited By KSCI : 1  (Citation Analysis)
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