Resumen de A local form for the automorphisms of the spectral unit ball

Pascal J. Thomas

• If F is an automorphism of ?_n, the n^2-dimensional spectral unit ball, we show that, in a neighborhood of any cyclic matrix of ?_n, 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.