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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. 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 -