JournalsrmiVol. 31, No. 2pp. 439–460

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

  • Yanqi Qiu

    Aix-Marseille Université, Marseille, France
On the effect of rearrangement on complex interpolation for families of Banach spaces cover
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Abstract

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\mathbb T that are invariant for complex interpolation at 0, they are precisely the origin-preserving inner functions.

Cite this article

Yanqi Qiu, On the effect of rearrangement on complex interpolation for families of Banach spaces. Rev. Mat. Iberoam. 31 (2015), no. 2, pp. 439–460

DOI 10.4171/RMI/840