The spectral continuity of essentially hyponormal operators
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If is a unital Banach algebra, then the spectrum can be viewed as a function σ : → , mapping each T ∈ to its spectrum σ(T), where S is the set, equipped with the Hausdorff metric, of all compact subsets of C. This paper is concerned with the continuity of the spectrum σ via Browder’s theorem. It is shown that σ is continuous when σ 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.
Abstract
If is a unital Banach algebra, then the spectrum can be viewed as a function σ : → , mapping each T ∈ to its spectrum σ(T), where S is the set, equipped with the Hausdorff metric, of all compact subsets of C. This paper is concerned with the continuity of the spectrum σ via Browder’s theorem. It is shown that σ is continuous when σ 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.
참고문헌 (21)
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