Saturating constructions for normed spaces

被引：0
|
作者：
S. J. Szarek
N. Tomczak-Jaegermann
机构：
[1] Université Pierre et Marie Curie,Equipe d’Analyse Fonctionnelle
[2] Case Western Reserve University,Department of Mathematics
[3] University of Alberta,Department of Mathematical and Statistical Sciences
来源：
Geometric & Functional Analysis GAFA | 2004年 / 14卷
关键词：
Normed Space; Space Versus; Convex Body; Large Section; Large Subspace;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove several results of the following type: given finite dimensional normed space V there exists another space X with log dim X = O(log dim V) and such that every subspace (or quotient) of X, whose dimension is not “too small,” contains a further subspace isometric to V. This sheds new light on the structure of such large subspaces or quotients (resp. large sections or projections of convex bodies) and allows us to solve several problems stated in the 1980s by V. Milman.
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页码：1352 / 1375
页数：23
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