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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm227-1-4,
author = {Daniel J. Fresen},
title = {Euclidean arrangements in Banach spaces},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {55-76},
zbl = {06446127},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm227-1-4}
}
Daniel J. Fresen. Euclidean arrangements in Banach spaces. Studia Mathematica, Tome 231 (2015) pp. 55-76. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm227-1-4/