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SPECTRAL CHARACTERIZATION OF ALGEBRAIC ELEMENTS

Published online by Cambridge University Press:  18 April 2001

THOMAS RANSFORD  and
MICHAEL WHITE
THOMAS RANSFORD
Affiliation:
Département de mathématiques et de statistique, Université Laval, Québec (QC), Canada G1K 7P4; e-mail: [email protected]
MICHAEL WHITE
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle upon Tyne NE1 7RU; e-mail: [email protected]
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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

(formula here)

We prove that the converse is also true, provided that A is semisimple.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 1 , January 2001 , pp. 77 - 82
Copyright
© The London Mathematical Society 2001

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