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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
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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

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