The unit ball of the complex P(H-3)
| dc.contributor.author | Grecu, B.C. | |
| dc.contributor.author | Muñoz-Fernández, Gustavo A. | |
| dc.contributor.author | Seoane Sepúlveda, Juan Benigno | |
| dc.date.accessioned | 2023-06-20T09:40:43Z | |
| dc.date.available | 2023-06-20T09:40:43Z | |
| dc.date.issued | 2009 | |
| dc.description.abstract | Let H be a two-dimensional complex Hilbert space and P(H-3) the space of 3-homogeneous polynomials on H. We give a characterization of the extreme points of its unit ball, B-P(3H), from which we deduce that the unit sphere of P(H-3) is the disjoint union of the sets of its extreme and smooth points. We also show that an extreme point of B-P(3H) remains extreme as considered as an element of B-L(3H). Finally we make a few remarks about the geometry of the unit ball of the predual of P(H-3) and give a characterization of its smooth points. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Marie Curie Intra European Fellowship | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/16965 | |
| dc.identifier.doi | 10.1007/s00209-008-0438-y | |
| dc.identifier.issn | 0025-5874 | |
| dc.identifier.relatedurl | http://www.springerlink.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50167 | |
| dc.journal.title | Mathematische Zeitschrift | |
| dc.language.iso | eng | |
| dc.page.final | 785 | |
| dc.page.initial | 775 | |
| dc.publisher | Springer | |
| dc.relation.projectID | MEIF-CT-2005-006958; MTM 2006-03531 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Unconditional constant | |
| dc.subject.keyword | Polynomial inequalities | |
| dc.subject.keyword | Trinomials | |
| dc.subject.keyword | Homogeneous polynomials | |
| dc.subject.keyword | Extreme points | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | The unit ball of the complex P(H-3) | |
| dc.type | journal article | |
| dc.volume.number | 263 | |
| dcterms.references | Aron, R.M., Cardwell, A., García, D., Zalduendo, I.: A multilinear Phelps’ Lemma. Proc. Am.Math. Soc. 135, 2549–2554 (2007) Aron, R.M., Hájek, P.: Zero sets of polynomials in several variables. Arch. Math. (Basel) 86(6), 561–568 (2006) Aron, R.M., Klimek, M.: Supremum norms for quadratic polynomials. Arch. Math. (Basel) 76, 73–80 (2001) Choi, Y.S., Kim, S.G., Ki, H.: Extreme polynomials and multilinear forms on l1. J. Math. Anal. Appl. 228(2), 467–482 (1998) Cobos, F., Kühn, T., Peetre, J.: Extreme points of the complex binary trilinear ball. Studia Math. 138(1), 81–92 (2000) Carando, D., Dimant, V., Sevilla-Peris, P.: Limit orders and multilinear forms on l p spaces. Publ. Res. Inst. Math. Sci. 42(2), 507–522 (2006) Dineen, S.: Complex analysis on infinite dimensional spaces. Springer Monographs in Mathematics, Springer-Verlag, London (1999) Dineen, S.: Extreme integral polynomials on a complex Banach space. Math. Scand. 92(1), 129–140 (2003) García, D., Grecu, B.C., Maestre, M.: Geometry in preduals of spaces of polynomials (2006, preprint) Grecu, B.C.: Extreme 2-homogeneous polynomials on Hilbert spaces. Quaest. Math. 25(4), 421–435 (2002) Grecu, B.C.: Geometry of three-homogeneous polynomials on real Hilbert spaces. J. Math. Anal. Appl. 246(1), 217–229 (2000) Grzaslewicz, R., John, K.: Extreme elements of the unit ball of bilinear operators on l 2 2 . Arch. Math. (Basel) 50(3), 264–269 (1988) Kim, S.G., Martin, M., Meri, J.: On the polynomial numerical index of the real spaces c0, 1 and ∞. J. Math. Anal. Appl. (2008, to appear) Konheim, A.G., Rivlin, T.J.: Extreme points of the unit ball in a space of real polynomials. Am. Math. Monthly 73, 505–507 (1966) Muñoz-Fernández, G.A., Seoane-Sepúlveda, J.B.: Geometry of Banach spaces of trinomials. J. Math. Anal. Appl. 340, 1069–1087 (2008) Neuwirth, S.: The maximum modulus of a trigonometric trinomial. arXiv:math/FA.0703236v1 Ryan,R.A.: Applications of topological tensor products to infinite dimensional holomorphy, Ph.D. Thesis, Trinity College Dublin (1980) | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | e85d6b14-0191-4b04-b29b-9589f34ba898 | |
| relation.isAuthorOfPublication.latestForDiscovery | e85d6b14-0191-4b04-b29b-9589f34ba898 |
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