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arXiv · 1304.1403

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

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

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Yanqi Qiu. 2013-04-04. On the effect of rearrangement on complex interpolation for families of Banach spaces. https://arxiv.org/abs/1304.1403

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