THE SPECTRAL CONTINUITY OF ESSENTIALLY HYPONORMAL OPERATORS

Title & Authors
THE SPECTRAL CONTINUITY OF ESSENTIALLY HYPONORMAL OPERATORS
Kim, An-Hyun; Ryu, Eun-Jin;

Abstract
If A is a unital Banach algebra, then the spectrum can be viewed as a function $\small{{\sigma}}$ : 𝕬 $\small{{\rightarrow}}$ 𝕾, mapping each T $\small{{\in}}$ 𝕬 to its spectrum $\small{{\sigma}(T)}$, where 𝕾 is the set, equipped with the Hausdorff metric, of all compact subsets of $\small{\mathbb{C}}$. This paper is concerned with the continuity of the spectrum $\small{{\sigma}}$ via Browder's theorem. It is shown that $\small{{\sigma}}$ is continuous when $\small{{\sigma}}$ 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;
Language
English
Cited by
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