A local form for the automorphisms of the spectral unit ball

• Autores: Pascal J. Thomas
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 59, Fasc. 3, 2008, págs. 321-324
• Idioma: inglés
• DOI: 10.1007/bf03191190
• Enlaces
  • Texto completo
• Resumen

  • If F is an automorphism of Ω n , then 2-dimensional spectral unit ball, we show that, in a neighborhood of any cyclic matrix of Ωn, the mapF 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.

• Referencias bibliográficas
  • L. Baribeau and T.J. Ransford, Nonlinear spectrumpreserving maps,Bull. London Math. Soc. 32 (2000), 8–14.
  • L. Baribeau and S. Roy, Caractérisation spectrale de la forme de Jordan,Linear Algebra Appl. 320 (2000), 183–191.
  • R.A. Horn and C.R. Johnson,Matrix Analysis, Cambridge University Press, Cambridge, 1985.
  • R.A. Horn and C.R. Johnson,Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
  • N. Nikolov, P.J. Thomas, and W. Zwonek, Discontinuity of the Lempert function and the Kobayashi-Royden metric of the spectral ball, (preprint,...
  • T.J. Ransford and M.C. White, Holomorphic selfmaps of the spectral unit ball,Bull. London Math. Soc. 23 (1991), 256–262.
  • J. Rostand, On the automorphisms of the spectral unit ball,Studia Math. 155 (2003), 207–230.
  • W. Zwonek, Proper holomorphic mappings of the spectral unit ball, (preprint, 2007), (arXiv:math.CV/0704.0614).