The real plank problem and some applications.
| dc.contributor.author | Muñoz-Fernández, Gustavo A. | |
| dc.contributor.author | Sarantopoulos, Y | |
| dc.contributor.author | Seoane-Sepúlveda, Juan B. | |
| dc.date.accessioned | 2023-06-20T03:30:44Z | |
| dc.date.available | 2023-06-20T03:30:44Z | |
| dc.date.issued | 2010 | |
| dc.description.abstract | K. Ball has proved the "complex plank problem": if (x(k))(k=1)(n) is a sequence of norm I vectors in a complex Hilbert space (H, (., .)), then there exists a unit vector x for which |< x,x(k)>| >= 1/root n, k = 1,...,n. In general, this result is not true on real Hilbert spaces. However, in special cases we prove that the same result holds true. In general, for some unit vector x we have derived the estimate |< x,x(k)>| >= max{root lambda(1)/n, 1/root lambda(n)n}, where lambda(1) is the smallest and lambda(n) is the largest eigenvalue of the Hermitian matrix A = [(x(j), x(k))], j, k = 1,...,n. We have also improved known estimates for the norms of homogeneous polynomials which are products of linear forms on real Hilbert spaces. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | C. Caratheodory | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/20003 | |
| dc.identifier.doi | 10.1090/S0002-9939-10-10295-0 | |
| dc.identifier.issn | 0002-9939 | |
| dc.identifier.officialurl | http://www.ams.org/journals/proc/2010-138-07/S0002-9939-10-10295-0/ | |
| dc.identifier.relatedurl | http://www.ams.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/43652 | |
| dc.issue.number | 7 | |
| dc.journal.title | Proceedings of the American Mathematical Society | |
| dc.language.iso | eng | |
| dc.page.final | 2521 | |
| dc.page.initial | 2521 | |
| dc.publisher | American Mathematical Society | |
| dc.relation.projectID | MTM2006-03531. | |
| dc.relation.projectID | No. 65/1602. | |
| dc.relation.projectID | MTM2006-03531. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Plank problems | |
| dc.subject.keyword | Polarization constants | |
| dc.subject.keyword | Product of linear functionals | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | The real plank problem and some applications. | |
| dc.type | journal article | |
| dc.volume.number | 138 | |
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| dspace.entity.type | Publication |
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