On the automorphisms of the spectral unit ball

Jérémie Rostand. "On the automorphisms of the spectral unit ball." Studia Mathematica 155.3 (2003): 207-230. <http://eudml.org/doc/284736>.

@article{JérémieRostand2003,
abstract = {Let Ω be the spectral unit ball of Mₙ(ℂ), that is, the set of n × n matrices with spectral radius less than 1. We are interested in classifying the automorphisms of Ω. We know that it is enough to consider the normalized automorphisms of Ω, that is, the automorphisms F satisfying F(0) = 0 and F'(0) = I, where I is the identity map on Mₙ(ℂ). The known normalized automorphisms are conjugations. Is every normalized automorphism a conjugation? We show that locally, in a neighborhood of a matrix with distinct eigenvalues, the answer is yes. We also prove that a normalized automorphism of Ω is a conjugation almost everywhere on Ω.},
author = {Jérémie Rostand},
journal = {Studia Mathematica},
keywords = {proper mapping; eigenvalue; holomorphic mappings; automorphism},
language = {eng},
number = {3},
pages = {207-230},
title = {On the automorphisms of the spectral unit ball},
url = {http://eudml.org/doc/284736},
volume = {155},
year = {2003},
}

TY - JOUR
AU - Jérémie Rostand
TI - On the automorphisms of the spectral unit ball
JO - Studia Mathematica
PY - 2003
VL - 155
IS - 3
SP - 207
EP - 230
AB - Let Ω be the spectral unit ball of Mₙ(ℂ), that is, the set of n × n matrices with spectral radius less than 1. We are interested in classifying the automorphisms of Ω. We know that it is enough to consider the normalized automorphisms of Ω, that is, the automorphisms F satisfying F(0) = 0 and F'(0) = I, where I is the identity map on Mₙ(ℂ). The known normalized automorphisms are conjugations. Is every normalized automorphism a conjugation? We show that locally, in a neighborhood of a matrix with distinct eigenvalues, the answer is yes. We also prove that a normalized automorphism of Ω is a conjugation almost everywhere on Ω.
LA - eng
KW - proper mapping; eigenvalue; holomorphic mappings; automorphism
UR - http://eudml.org/doc/284736
ER -