Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-28T06:50:42.962Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)