Unconditional bases in tensor products of Hilbert spaces
We prove that a tensor norm alpha (defined on tensor products of Hilbert spaces) is the Hilbert-Schmidt norm if and only if l(2) circle times(...)circle times l(2), endowed with the norm alpha, has an unconditional basis. This extends a classical result of Kwapien and Pelczynski. The symmetric versi...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2005 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/49597 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/49597 |
| Access Level: | acceso abierto |
| Palabra clave: | 517.98 Banach-spaces Polynomials Forms Hilbert-Schmidt operators Unconditional basis Tensor products P-summing operators Multilinear operators Análisis funcional y teoría de operadores |
| Sumario: | We prove that a tensor norm alpha (defined on tensor products of Hilbert spaces) is the Hilbert-Schmidt norm if and only if l(2) circle times(...)circle times l(2), endowed with the norm alpha, has an unconditional basis. This extends a classical result of Kwapien and Pelczynski. The symmetric version of that statement follows, and this extends a recent result of Defant, Diaz, Garcia and Maestre. |
|---|