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Lookup NU author(s): Dr Michael White
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It is known that if a is an algebraic element of a Banach algebra A, then its spectrum σ(a) is finite, and there exists γ > 0 such that the Hausdorff distance to spectra of nearby elements satisfies Δ(σ(a + x), σ(a)) = O(∥x∥γ) as x → 0. We prove that the converse is also true, provided that A is semisimple.
Author(s): White M; Ransford T
Publication type: Article
Publication status: Published
Journal: Bulletin of the London Mathematical Society
ISSN (print): 0024-6093
ISSN (electronic): 1469-2120
Publisher: Oxford University Press
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