A local form for the automorphisms of the spectral unit ball

Pascal J. Thomas (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

If F is an automorphism of the spectral unit ball, we show that, in a neighborhood of any cyclic (i.e. non-derogatory) matrix of the ball, the map F can be written as conjugation by a holomorphically varying non singular matrix. This provides a shorter proof of a theorem of J. Rostand, with a slightly stronger result.

Mots clés: biholomorphisms; spectral ball

Domaines: Variables complexes [math.CV]; Analyse fonctionnelle [math.FA]

Pascal J. Thomas. A local form for the automorphisms of the spectral unit ball. Collectanea Mathematica, 2008, 59 (3), pp.321-324. ⟨hal-00321229⟩