Euclidean arrangements in Banach spaces

• Autorzy: Daniel J. Fresen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 52A23: Asymptotic theory of convex bodies
• 52A21: Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
• 46B20: Geometry and structure of normed linear spaces
• 46B07: Local theory of Banach spaces
• 46B09: Probabilistic methods in Banach space theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 227
• Numer: 1
• Strony: 55-76

Daty

wydano

2015

Twórcy

autor

Daniel J. Fresen

• Department of Mathematics, Yale University, New Haven, CT, U.S.A.

Identyfikatory

DOI

10.4064/sm227-1-4