Euclidean arrangements in Banach spaces

Daniel J. Fresen. "Euclidean arrangements in Banach spaces." Studia Mathematica 227.1 (2015): 55-76. <http://eudml.org/doc/285607>.

@article{DanielJ2015,
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.},
author = {Daniel J. Fresen},
journal = {Studia Mathematica},
keywords = {Dvoretzky's theorem; Kashin decomposition; cotype; John's position; sparse vector},
language = {eng},
number = {1},
pages = {55-76},
title = {Euclidean arrangements in Banach spaces},
url = {http://eudml.org/doc/285607},
volume = {227},
year = {2015},
}

TY - JOUR
AU - Daniel J. Fresen
TI - Euclidean arrangements in Banach spaces
JO - Studia Mathematica
PY - 2015
VL - 227
IS - 1
SP - 55
EP - 76
AB - 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.
LA - eng
KW - Dvoretzky's theorem; Kashin decomposition; cotype; John's position; sparse vector
UR - http://eudml.org/doc/285607
ER -