Complemented Subspaces of L_p Determined by Partitions and Weights
| dc.creator | Alspach, Dale | |
| dc.creator | Tong, Simei | |
| dc.date | 2002-10-15 | |
| dc.date.accessioned | 2026-07-07T04:51:58Z | |
| dc.date.available | 2026-07-07T04:51:58Z | |
| dc.description | Many of the known complemented subspaces of L_p have realizations as sequence spaces. In this paper a systematic approach to defining these spaces which uses partitions and weights is introduced. This approach gives a unified description of many well-known complemented subspaces of L_p. It is proved that the class of spaces with such norms is stable under (p,2) sums. By introducing the notion of an envelope norm, we obtain a necessary condition for a Banach sequence space with norm given by partitions and weights to be isomorphic to a subspace of L_p. Using this we define a space Y_n with norm given by partitions and weights with distance to any subspace of L_p growing with n. This allows us to construct an example of a Banach space with norm given by partitions and weights which is not isomorphic to a subspace of L_p. | |
| dc.identifier | https://arxiv.org/abs/math/0210228 | |
| dc.identifier | http://arxiv.org/abs/math/0210228 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65301 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B20 Primary 46E30 Secondary | |
| dc.title | Complemented Subspaces of L_p Determined by Partitions and Weights | |
| dc.type | text |