2013/04/04 by Yanqi Qiu, Qiu, Yanqi
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1304.1403
openalex publication_date 2013/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.