Geometry of Banach spaces of trinomials
| dc.contributor.author | Muñoz-Fernández, Gustavo A. | |
| dc.contributor.author | Seoane Sepúlveda, Juan Benigno | |
| dc.date.accessioned | 2023-06-20T09:41:37Z | |
| dc.date.available | 2023-06-20T09:41:37Z | |
| dc.date.issued | 2008-04-15 | |
| dc.description.abstract | For each pair of numbers m, n epsilon N with m > n, we consider the norm on R-3 given by parallel to(a, b, c)parallel to m,n = sup{vertical bar ax(m) +bx(n) +C vertical bar: x epsilon [-1, 1]} for every (a, b, c) epsilon R-3. We investigate some geometrical properties of these norms. We provide an explicit formula for parallel to center dot parallel to m,n, a full description of the extreme points of the corresponding unit balls and a parametrization and a plot of their unit spheres. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | MTM 2006-0353 | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17087 | |
| dc.identifier.doi | 10.1016/j.jmaa.2007.09.010 | |
| dc.identifier.issn | 0022-247X | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0022247X07011237 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50195 | |
| dc.issue.number | 2 | |
| dc.journal.title | Journal of Mathematical Analysis and Applications | |
| dc.language.iso | eng | |
| dc.page.final | 1087 | |
| dc.page.initial | 1069 | |
| dc.publisher | Academic Press | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Convexity | |
| dc.subject.keyword | Extreme points | |
| dc.subject.keyword | Polynomial norms | |
| dc.subject.keyword | Trinomials | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Geometry of Banach spaces of trinomials | |
| dc.type | journal article | |
| dc.volume.number | 340 | |
| dcterms.references | R.M. Aron, M. Klimek, Supremum norms for quadratic polynomials, Arch. Math. (Basel) 76 (2001) 73–80. Y.S. Choi, S.G. Kim, The unit ball of P(2l2 2 ), Arch. Math. (Basel) 76 (1998) 472–480. Y.S. Choi, S.G. Kim, Smooth points of the unit ball of the space P(2l1), Results Math. 36 (1999) 26–33. Y.S. Choi, S.G. Kim, Exposed points of the unit balls of the spaces P(2l2p) (p = 1, 2,∞), Indian J. Pure Appl. Math. 35 (2004) 37–41. B.C. Grecu, Geometry of homogeneous polynomials on two-dimensional real Hilbert spaces, J. Math. Anal. Appl. 293 (2) (2004) 578–588. B.C. Grecu, Extreme 2-homogeneous polynomials on Hilbert spaces, Quaest. Math. 25 (4) (2002) 421–435. B.C. Grecu, Geometry of 2-homogeneous polynomials on lp spaces, 1<p<∞, J. Math. Anal. Appl. 273 (2) (2002) 262–282. B.C. Grecu, Smooth 2-homogeneous polynomials on Hilbert spaces, Arch. Math. (Basel) 76 (6) (2001) 445–454. B.C. Grecu, Geometry of three-homogeneous polynomials on real Hilbert spaces, J. Math. Anal. Appl. 246 (1) (2000) 217–229. B.C. Grecu, G.A. Muñoz-Fernández, J.B. Seoane-Sepúlveda, The unit ball of the complex P(3H), preprint. G. Klimek, M. Klimek, Discovering Curves and Surfaces with Maple, New York, 1997. A.G. Konheim, T.J. Rivlin, Extreme points of the unit ball in a space of real polynomials, Amer. Math. Monthly 73 (1966) 505–507. G.A. Muñoz-Fernández, Y. Sarantopoulos, J.B. Seoane-Sepúlveda, An application of the Krein–Milman Theorem to Bernstein and Markov inequalities, preprint. S. Neuwirth, The maximum modulus of a trigonometric trinomial, arXiv:math/FA0703236v1. S. Révész, Minimization of maxima of nonnegative and positive definite cosine polynomials with prescribed first coefficients, Acta Sci. Math. (Szeged) 60 (1995) 589–608. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | e85d6b14-0191-4b04-b29b-9589f34ba898 | |
| relation.isAuthorOfPublication.latestForDiscovery | e85d6b14-0191-4b04-b29b-9589f34ba898 |
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