On convexified packing and entropy duality
| dc.creator | Artstein, S. | |
| dc.creator | Milman, V. | |
| dc.creator | Szarek, S. J. | |
| dc.creator | Tomczak-Jaegermann, N. | |
| dc.date | 2004-07-14 | |
| dc.date.accessioned | 2026-07-07T05:10:17Z | |
| dc.date.available | 2026-07-07T05:10:17Z | |
| dc.description | A 1972 duality conjecture due to Pietsch asserts that the entropy numbers of a compact operator acting between two Banach spaces and those of its adjoint are (in an appropriate sense) equivalent. This is equivalent to a dimension free inequality relating covering (or packing) numbers for convex bodies to those of their polars. The duality conjecture has been recently proved (see math.FA/0407236) in the central case when one of the Banach spaces is Hilbertian, which - in the geometric setting - corresponds to a duality result for symmetric convex bodies in Euclidean spaces. In the present paper we define a new notion of "convexified packing," show a duality theorem for that notion, and use it to prove the duality conjecture under much milder conditions on the spaces involved (namely, that one of them is K-convex). | |
| dc.description | 6 p., LATEX | |
| dc.identifier | https://arxiv.org/abs/math/0407238 | |
| dc.identifier | http://arxiv.org/abs/math/0407238 | |
| dc.identifier | Geom. Funct. Anal. 14 (2004), no. 5, 1134-1141. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71883 | |
| dc.subject | Functional Analysis | |
| dc.subject | Metric Geometry | |
| dc.subject | 46B10; 46B07; 46B50; 47A05; 52C17; 51F99 | |
| dc.title | On convexified packing and entropy duality | |
| dc.type | text |