- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:47
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
31
2015
2
On the effect of rearrangement on complex interpolation for families of Banach spaces
Yanqi
Qiu
Aix-Marseille Université, MARSEILLE CEDEX 13, FRANCE
Complex interpolation method for families, rearrangement, matrix valued outer functions, Toeplitz operator, duality
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 $\mathbb T$ that are invariant for complex interpolation at 0, they are precisely the origin-preserving inner functions.
Functional analysis
439
460
10.4171/RMI/840
http://www.ems-ph.org/doi/10.4171/RMI/840