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Saturating constructions for normed spaces II |
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| Authors: | Stanislaw J Szarek Nicole Tomczak-Jaegermann |
| Institution: | a Department of Mathematics, Case Western Reserve University, 10900 Euclid Ave, Cleveland, OH 44106-7058, USA b Equipe d’Analyse Fonctionnelle, BP 186, Université Pierre et Marie Curie, 75252 Paris, France c Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1 |
| Abstract: | We prove several results of the following type: given finite-dimensional normed space V possessing certain geometric property there exists another space X having the same property and such that (1)  and (2) every subspace of X, whose dimension is not “too small”, contains a further well-complemented subspace nearly isometric to V. This sheds new light on the structure of large subspaces or quotients of normed spaces (resp., large sections or linear images of convex bodies) and provides definitive solutions to several problems stated in the 1980s by Milman. |
| Keywords: | Normed spaces Subspaces Quotients Saturation Cotype K-convexity Global properties Random convex bodies |
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