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Spectral characterization of algebraic elements

Lookup NU author(s): Dr Michael White

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Abstract

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.

Publication metadata

Author(s): White M; Ransford T

Publication type: Article

Publication status: Published

Journal: Bulletin of the London Mathematical Society

Year: 2001

Volume: 33

Issue: 1

Pages: 77-82

ISSN (print): 0024-6093

ISSN (electronic): 1469-2120

Publisher: Oxford University Press

URL: http://dx.doi.org/10.1112/blms/33.1.77

DOI: 10.1112/blms/33.1.77

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