Product spaces generated by bilinear maps and duality

In this paper we analyse a definition of a product of Banach spaces that is naturally associated by duality with a space of operators that can be considered as a generalization of the notion of space of multiplication operators. This dual relation allows to understand several constructions coming fr...

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Detalles Bibliográficos
Autor: Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154
Tipo de recurso: artículo
Fecha de publicación:2015
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:10251/77545
Acceso en línea:https://riunet.upv.es/handle/10251/77545
Access Level:acceso abierto
Palabra clave:Banach space
Product
Multiplication operator
Duality
Banach function space
Hadamard product
Lipschitz map
Integration
Vector measure
MATEMATICA APLICADA
Descripción
Sumario:In this paper we analyse a definition of a product of Banach spaces that is naturally associated by duality with a space of operators that can be considered as a generalization of the notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different fields of functional analysis that can be seen as instances of the abstract one when a particular product is considered. Some relevant examples and applications are shown, regarding pointwise products of Banach function spaces, spaces of integrable functions with respect to vector measures, spaces of operators, multipliers on Banach spaces of analytic functions and spaces of Lipschitz functions.