Saturating Constructions for Normed Spaces II

Details Saturating Constructions for Normed Spaces II Saturating Constructions for Normed Spaces II

2004-07-14

arxiv.org/abs/math/0407234v1

J. Funct. Anal. 221 (2005), no. 2, 407-438.

Mathematics

Functional Analysis

35 p., LATEX; the paper is a follow up on math.FA/0407233

Scientific paper

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) log (dim X) = O(log (dim V)) 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 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 II 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 II, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Saturating Constructions for Normed Spaces II will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-335264