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Subspaces and Orthogonal Decompositions Generated by Bounded Orthogonal Systems
| Content Provider | Semantic Scholar |
|---|---|
| Author | Guédon, Olivier Mendelson, Shahar Pajor, Alain Tomczak-Jaegermann, Nicole |
| Copyright Year | 2007 |
| Abstract | We investigate properties of subspaces of L2 spanned by subsets of a finite orthonormal system bounded in the L∞ norm. We first prove that there exists an arbitrarily large subset of this orthonormal system on which the L1 and the L2 norms are close, up to a logarithmic factor. Considering for example the Walsh system, we deduce the existence of two orthogonal subspaces of L2n, complementary to each other and each of dimension roughly n/2, spanned by ± 1 vectors (i.e. Kashin's splitting) and in logarithmic distance to the Euclidean space. The same method applies for p > 2, and, in connection with the Λp problem (solved by Bourgain), we study large subsets of this orthonormal system on which the L2 and the Lp norms are close (again, up to a logarithmic factor). |
| Starting Page | 269 |
| Ending Page | 283 |
| Page Count | 15 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s11117-006-2059-1 |
| Volume Number | 11 |
| Alternate Webpage(s) | http://maths-people.anu.edu.au/~mendelso/papers/GMPT-Hadamard-31a-08.pdf |
| Alternate Webpage(s) | http://wwwmaths.anu.edu.au/~mendelso/papers/GMPT-fin.pdf |
| Alternate Webpage(s) | http://perso-math.univ-mlv.fr/users/pajor.alain/recherche/docs/GMPT-Hadamard.pdf |
| Alternate Webpage(s) | http://www.math.jussieu.fr/~guedon/Articles/06/GMPT.pdf |
| Alternate Webpage(s) | http://maths-people.anu.edu.au/~mendelso/papers/GMPT-fin.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
