Coordinate restrictions of linear operators in $l_2^n$
| dc.creator | Vershynin, R. | |
| dc.date | 2000-11-28 | |
| dc.date.accessioned | 2026-07-07T04:38:52Z | |
| dc.date.available | 2026-07-07T04:38:52Z | |
| dc.description | This paper addresses the problem of improving properties of a linear operator u in $l_2^n$ by restricting it onto coordinate subspaces. We discuss how to reduce the norm of u by a random coordinate restriction, how to approximate u by a random operator with small "coordinate" rank, how to find coordinate subspaces where u is an isomorphism. The first problem in this list provides a probabilistic extension of a suppression theorem of Kashin and Tzafriri, the second one is a new look at a result of Rudelson on the random vectors in the isotropic position, the last one is the recent generalization of the Bourgain-Tzafriri's invertibility principle. The main point is that all the results are independent of n, the situation is instead controlled by the Hilbert-Schmidt norm of u. As an application, we provide an almost optimal solution to the problem of harmonic density in harmonic analysis, and a solution to the reconstruction problem for communication networks which deliver data with random losses. | |
| dc.identifier | https://arxiv.org/abs/math/0011232 | |
| dc.identifier | http://arxiv.org/abs/math/0011232 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60450 | |
| dc.subject | Functional Analysis | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Probability | |
| dc.subject | 46B09 (60G50, 43A46, 43A46) | |
| dc.title | Coordinate restrictions of linear operators in $l_2^n$ | |
| dc.type | text |