Unconditionality for m-homogeneous polynomials on l(infinity)n
[EN] Let x(m, n) be the unconditional basis constant of the monomial basis Z alpha, alpha is an element of N(0)n with vertical bar alpha vertical bar = m, of the Banach space of all m-homogeneous polynomials inn complex variables, endowed with the supremum norm on the n-dimensional unit polydisc Dn....
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/94469 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/94469 |
| Access Level: | acceso abierto |
| Palabra clave: | Unconditional basis constant Homogeneous polynomials MATEMATICA APLICADA |
| Sumario: | [EN] Let x(m, n) be the unconditional basis constant of the monomial basis Z alpha, alpha is an element of N(0)n with vertical bar alpha vertical bar = m, of the Banach space of all m-homogeneous polynomials inn complex variables, endowed with the supremum norm on the n-dimensional unit polydisc Dn. We prove that the quotient of sup(m) m root sup(m)chi(m, n) and root n/log n tends to 1 as n -> infinity. This reflects a quite precise dependence of chi(m, n) on the degree m of the polynomials and their number n of variables. Moreover, we give an analogous formula for m-linear forms, a reformulation of our results in terms of tensor products, and as an application a solution for a problem on Bohr radii. |
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