Euclidean arrangements in Banach spaces

Volume 227 / 2015

Daniel J. Fresen Studia Mathematica 227 (2015), 55-76 MSC: 46B20, 52A23, 46B09, 52A21, 46B07. DOI: 10.4064/sm227-1-4


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.


  • Daniel J. FresenDepartment of Mathematics
    Yale University
    New Haven, CT, U.S.A.

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