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SPECTRAL CHARACTERIZATION OF ALGEBRAIC ELEMENTS
Published online by Cambridge University Press: 18 April 2001
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.
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- © The London Mathematical Society 2001
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