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arXiv · 1309.5526

Euclidean arrangements in Banach spaces

Daniel J. Fresen
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Abstract

We study the way in which the Euclidean subspaces of a Banach space fit together, somewhat in the spirit of the Kašin 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.

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Daniel J. Fresen. 2015-05-04. Euclidean arrangements in Banach spaces. https://arxiv.org/abs/1309.5526

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