On the effect of rearrangement on complex interpolation for families of Banach spaces

• Yanqi Qiu ^[1]
  1. [1] Aix-Marseille University

     Aix-Marseille University

     Arrondissement de Marseille, Francia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 31, Nº 2, 2015, págs. 439-460
• Idioma: inglés
• DOI: 10.4171/RMI/840
• Texto completo no disponible (Saber más ...)
• Resumen

  • We give a new proof to show that the complex interpolation for families of Banach spaces is not stable under rearrangement of the given family on the boundary, although, by a result due to Coifman, Cwikel, Rochberg, Sagher and Weiss, it is stable when the latter family takes only 2 values. The non-stability for families taking 3 values was first obtained by Cwikel and Janson. Our method links this problem to the theory of matrix-valued Toeplitz operator and we are able to characterize all the transformations on T that are invariant for complex interpolation at 0, they are precisely the origin-preserving inner functions.