Geodesic
Euclidean arrangements in Banach spaces
Daniel J. Fresen1
1 Department of Mathematics Yale University New Haven, CT, U.S.A.
Studia Mathematica, Tome 227 (2015) no. 1, pp. 55-76 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm227-1-4
Keywords: study which euclidean subspaces banach space fit together somewhat spirit kashin decomposition main tool introduce estimate regarding convex hull convex body johns position euclidean ball given radius which leads simplified proof randomized isomorphic dvoretzky theorem results include characterization spaces nontrivial cotype terms arrangements euclidean subspaces

Daniel J. Fresen 1

1 Department of Mathematics Yale University New Haven, CT, U.S.A. 
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Daniel J. Fresen. Euclidean arrangements in Banach spaces. Studia Mathematica, Tome 227 (2015) no. 1, pp. 55-76. doi: 10.4064/sm227-1-4

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