Euclidean arrangements in Banach spaces
Volume 227 / 2015
Studia Mathematica 227 (2015), 55-76
MSC: 46B20, 52A23, 46B09, 52A21, 46B07.
DOI: 10.4064/sm227-1-4
Abstract
We study the way in which the Euclidean subspaces of a Banach space fit together, somewhat in the spirit of the Kashin decomposition. The main tool that we introduce is an estimate regarding the convex hull of a convex body in John's position with a Euclidean ball of a given radius, which leads to a new and simplified proof of the randomized isomorphic Dvoretzky theorem. Our results also include a characterization of spaces with nontrivial cotype in terms of arrangements of Euclidean subspaces.
