Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-24T10:45:13.242Z Has data issue: false hasContentIssue false
  • English
  • Français

NON-LINEAR SPECTRUM-PRESERVING MAPS

Published online by Cambridge University Press:  01 January 2000

LINE BARIBEAU  and
THOMAS RANSFORD
LINE BARIBEAU
Affiliation:
Département de mathématiques et de statistique, Université Laval, Québec (QC), Canada G1K 7P4
THOMAS RANSFORD
Affiliation:
Département de mathématiques et de statistique, Université Laval, Québec (QC), Canada G1K 7P4
Get access

Abstract

Let [Mscr ]n denote the space of complex n×n matrices, and let Ωn denote the spectral unit ball of [Mscr ]n, namely the set of matrices in [Mscr ]n whose eigenvalues lie within the open unit disc. As a step towards the eventual classification of the holomorphic automorphisms of Ωn, we prove that every such automorphism F satisfying F(0) = 0 and F′(0) = I has the property that F(x) is conjugate to x for each x∈Ωn. This result is obtained by combining earlier work of Ransford and White with a general theorem about spectrum-preserving maps proved in this paper.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 1 , January 2000 , pp. 8 - 14
Copyright
© The London Mathematical Society 2000

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.)