%0 Journal Article %1 ivanisvili2020rademacher %A Ivanisvili, Paata %A van Handel, Ramon %A Volberg, Alexander %D 2020 %K mathematics probability readings theory %T Rademacher type and Enflo type coincide %U http://arxiv.org/abs/2003.06345 %X 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 long-standing open problem in Banach space theory. The proof is based on a novel dimension-free analogue of Pisier's inequality on the discrete cube.

@article{ivanisvili2020rademacher, 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 long-standing open problem in Banach space theory. The proof is based on a novel dimension-free analogue of Pisier's inequality on the discrete cube.}, added-at = {2020-03-20T20:11:01.000+0100}, author = {Ivanisvili, Paata and van Handel, Ramon and Volberg, Alexander}, biburl = {https://www.bibsonomy.org/bibtex/2dca9bdcd396237d6221f8a679fb0d8d6/kirk86}, description = {[2003.06345] Rademacher type and Enflo type coincide}, interhash = {b7da2136dee1ac21ea5f54bb04757756}, intrahash = {dca9bdcd396237d6221f8a679fb0d8d6}, keywords = {mathematics probability readings theory}, note = {cite arxiv:2003.06345Comment: 10 pages}, timestamp = {2020-03-20T20:11:01.000+0100}, title = {Rademacher type and Enflo type coincide}, url = {http://arxiv.org/abs/2003.06345}, year = 2020 }