Ideal structures in vector-valued polynomial spaces
This paper is concerned with the study of geometric structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of n-homogeneous polynomials, 'P-w((n) E, F), which are weakly continuous on bounded sets, is an HB-subspace or an M(1, C)-ideal in th...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/23072 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/23072 |
| Access Level: | acceso abierto |
| Palabra clave: | 517.98 HB-subspaces Homogeneous polynomials Weakly continuous on bounded sets polynomials Análisis funcional y teoría de operadores |
| Sumario: | This paper is concerned with the study of geometric structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of n-homogeneous polynomials, 'P-w((n) E, F), which are weakly continuous on bounded sets, is an HB-subspace or an M(1, C)-ideal in the space of continuous n-homogeneous polynomials, P((n) E, F). We establish sufficient conditions under which the problem can be positively solved. Some examples are given. We also study when some ideal structures pass from P-w((n) E, F) as an ideal in P((n) E, F) to the range space F as an ideal in its bidual F**. |
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