The natural rearrangement invariant structure on tensor products
| dc.contributor.author | Fernández González, Carlos | |
| dc.contributor.author | Palazuelos Cabezón, Carlos | |
| dc.contributor.author | Pérez García, David | |
| dc.date.accessioned | 2023-06-20T09:45:20Z | |
| dc.date.available | 2023-06-20T09:45:20Z | |
| dc.date.issued | 2008 | |
| dc.description.abstract | We prove that the only rearrangement invariant (r.i.) spaces for which there exists a crossnorm verifying that the tensor product of these spaces preserves the "natural" r.i. space structure, in the sense that it makes the multiplication operator B a topological isomorphism, are the Lp spaces. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | MEC FPU Fellowship | |
| dc.description.sponsorship | I+D MCYT | |
| dc.description.sponsorship | Complutense-Santander | |
| dc.description.sponsorship | Comunidad de Madrid | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17793 | |
| dc.identifier.doi | http:dx.doi.org/10.1016/j.jmaa.2008.01.016 | |
| dc.identifier.issn | 0022-247X | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0022247X0800036X | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50306 | |
| dc.issue.number | 1 | |
| dc.journal.title | Journal of Mathematical Analysis and Applications | |
| dc.language.iso | eng | |
| dc.page.final | 47 | |
| dc.page.initial | 40 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | (MTM 2004-08080-C02-01) | |
| dc.relation.projectID | (MTM 2005-00082) | |
| dc.relation.projectID | COMPLUTENSESANTANDER (PR27/05-14045) | |
| dc.relation.projectID | Comunidad de Madrid grant UCM (910346) | |
| dc.relation.projectID | Beca-COMPLUTENSE 2005 | |
| dc.relation.projectID | Spanish Ramón y Cajal Project | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Crossnorms in tensor product | |
| dc.subject.keyword | Rearrangement invariant spaces | |
| dc.subject.keyword | Lp spaces | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | The natural rearrangement invariant structure on tensor products | |
| dc.type | journal article | |
| dc.volume.number | 343 | |
| dcterms.references | Z. Altshuler, Characterization of co and lp among Banach spaces with symmetric basis, Israel J. Math. 24 (1976) 39–44. T. Andô, On products of Orlicz spaces, Math. Ann. 140 (1960) 174–186. S.V. Astashkin, Tensor product in symmetric function spaces, Collect. Math. 48 (1997) 375–391. S.V. Astashkin, L. Maligranda, E.M. Semenov, Multiplicator space and complemented subspaces of rearrangement invariant space, J. Funct. Anal. 202 (2003) 247–276. A. Defant, K. Floret, Tensor Norms and Operator Ideals, North-Holland, Amsterdam, 1993. A. Defant, D. Pérez-García, A tensor norm preserving unconditionality for Lp-spaces, Trans. Amer. Math. Soc., in press. D.H. Fremlin, Tensor products of Archimedean vector lattices, Amer. J. Math. 94 (1972) 777–798. D.H. Fremlin, Tensor products of Banach lattices, Math. Ann. 211 (1974) 87–106. B.R. Gelbaum, J. Gil de Lamadrid, Bases of tensor products of Banach spaces, Pacific J. Math. 11 (1961) 1281–1286. F.L. Hernandez, E.M. Semenov, Subspaces generated by translations in rearrangement invariant spaces, J. Funct. Anal. 169 (1999) 52–80. J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces I and II, Springer-Verlag, 1996. M. Milman, Some new function spaces and their tensor product, Notas Mat. 20 (1978) 1–128. M. Milman, Tensor products of function spaces, Bull. Amer. Math. Soc. 82 (1976) 626–628. M. Milman, Embeddings of Lorentz–Marcinkiewicz spaces with mixed norms, Anal. Math. 4 (3) (1978) 215–223. M. Milman, Embeddings of L(p, q) spaces and Orlicz spaces with mixed norms, Notas Mat. 13 (1977) 1–7. R. O’Neil, Integral transforms and tensor products on Orlicz spaces and L(p, q) spaces, J. Anal. Math. 21 (1968) 1–276. C.J. Read, When E and E[E] are isomorphic, in: Geometry of Banach Spaces, Strobl, 1989, in: London Math. Soc. Lecture Note Ser., vol. 158, Cambridge Univ. Press, Cambridge, 1990, pp. 245–252. A. Torchinsky, Interpolation of operations and Orlicz classes, Studia Math. 59 (2) (1976/1977) 177–207. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 09970d9e-6722-4f02-aac0-023cf9867638 | |
| relation.isAuthorOfPublication | 5edb2da8-669b-42d1-867d-8fe3144eb216 | |
| relation.isAuthorOfPublication.latestForDiscovery | 09970d9e-6722-4f02-aac0-023cf9867638 |
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