Spectral characterization of algebraic elements

Authors
Ransford, T White, M
Citation
T. Ransford et M. White, Spectral characterization of algebraic elements, B LOND MATH, 33, 2001, pp. 77-82
Citations number
6
Categorie Soggetti
Mathematics
Journal title
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
ISSN journal
00246093 → ACNP
Volume
33
Year of publication
2001
Part
1
Pages
77 - 82
Database
ISI
SICI code
0024-6093(200101)33:<77:SCOAE>2.0.ZU;2-K
Abstract
It is known that if a is an algebraic element of a Banach algebra A, then i ts spectrum a(a) is finite, and there exists gamma > 0 such that the Hausdo rff distance to spectra of nearby elements satisfies. Delta(sigma (a + x), sigma (a)) = O(parallel tox parallel to (gamma)) as x --> 0. We prove that the converse is also true, provided that A is semisimple.