Extension of polynomials defined on subspaces.
| dc.contributor.author | Fernandez Unzueta, Maite | |
| dc.contributor.author | Prieto Yerro, M. Ángeles | |
| dc.date.accessioned | 2023-06-20T00:21:47Z | |
| dc.date.available | 2023-06-20T00:21:47Z | |
| dc.date.issued | 2010 | |
| dc.description.abstract | Let k is an element of N and let E be a Banach space such that every k-homogeneous polynomial defined on a subspace of E has an extension to E. We prove that every norm one k-homogeneous polynomial, defined on a subspace, has an extension with a uniformly bounded norm. The analogous result for holomorphic functions of bounded type is obtained. We also prove that given an arbitrary subspace F subset of E. there exists a continuous morphism phi(k,F) : P((k)F) -> P((k)E) satisfying phi(k,F)(P)vertical bar(F) = P, if and only E is isomorphic to a Hilbert space. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | CONACyT | |
| dc.description.sponsorship | MEC | |
| dc.description.sponsorship | UCM | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17522 | |
| dc.identifier.doi | 10.1017/S0305004110000022 | |
| dc.identifier.issn | 0305-0041 | |
| dc.identifier.officialurl | http://journals.cambridge.org/abstract_S0305004110000022 | |
| dc.identifier.relatedurl | http://www.cambridge.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/42457 | |
| dc.issue.number | 3 | |
| dc.journal.title | Mathematical Proceedings of the Cambridge Philosophical Society | |
| dc.language.iso | eng | |
| dc.page.final | 518 | |
| dc.page.initial | 505 | |
| dc.publisher | Cambridge Univ Press | |
| dc.relation.projectID | P48363-F | |
| dc.relation.projectID | MTM 2006-03531 | |
| dc.relation.projectID | 910626. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Homogeneous polynomial | |
| dc.subject.keyword | Holomorphic functions of bounded type | |
| dc.subject.keyword | Extension theorems | |
| dc.subject.keyword | Extension morphism | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Extension of polynomials defined on subspaces. | |
| dc.type | journal article | |
| dc.volume.number | 148 | |
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| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | f2a43f90-b551-412e-a95d-2587bbfaa27d | |
| relation.isAuthorOfPublication.latestForDiscovery | f2a43f90-b551-412e-a95d-2587bbfaa27d |
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