Rademacher type and Enflo type coincide
Abstract
A nonlinear analogue of the Rademacher type of a Banach space was introduced in classical work of Enflo. The key feature of Enflo type is that its definition uses only the metric structure of the Banach space, while the definition of Rademacher type relies on its linear structure. We prove that Rademacher type and Enflo type coincide, settling a longstanding open problem in Banach space theory. The proof is based on a novel dimensionfree analogue of Pisier's inequality on the discrete cube.
 Publication:

arXiv eprints
 Pub Date:
 March 2020
 arXiv:
 arXiv:2003.06345
 Bibcode:
 2020arXiv200306345I
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Metric Geometry;
 46B09;
 46B07;
 60E15
 EPrint:
 11 pages