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...

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Detalles Bibliográficos
Autores: Dimant, Verónica, Lassalle, Silvia, Prieto Yerro, M. Ángeles
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
Descripción
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**.