Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

On the automorphisms of the spectral unit ball

100%

Rostand J.

Studia Mathematica

2003

tom 155

nr 3

207-230

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.

Ograniczanie wyników

1 Studia Mathematica

1 Rostand J.

1 2003

Wyniki wyszukiwania

On the automorphisms of the spectral unit ball