Mathematics – Functional Analysis
Scientific paper
1992-04-21
Mathematics
Functional Analysis
Scientific paper
We prove that Hilbert space is distortable and, in fact, arbitrarily distortable. This means that for all lambda >1 there exists an equivalent norm |.| on l_2 such that for all infinite dimensional subspaces Y of l_2 there exist x,y in Y with ||x||_2 = ||y||_2 =1 yet |x| >lambda |y|. We also prove that if X is any infinite dimensional Banach space with an unconditional basis then the unit sphere of X and the unit sphere of l_1 are uniformly homeomorphic if and only if X does not contain l_infty^n's uniformly.
Odell Edward
Schlumprecht Thomas
No associations
LandOfFree
The Distorion Problem 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 The Distorion Problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Distorion Problem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-481172