Saturating Constructions for Normed Spaces

Details Saturating Constructions for Normed Spaces Saturating Constructions for Normed Spaces

2004-07-14

arxiv.org/abs/math/0407233v1

Geom. Funct. Anal. 14 (2004), no. 6, 1352-1375.

Mathematics

Functional Analysis

27 p., LATEX; see also a follow up paper: math.FA/0407234

Scientific paper

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 to solve several problems stated in the 1980s by V. Milman. The proofs are probabilistic and depend on careful analysis of images of convex sets under Gaussian linear maps.

Affiliated with

Also associated with

No associations

Rating

Saturating Constructions for Normed Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Saturating Constructions for Normed Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Saturating Constructions for Normed Spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-335258