Extending and factorizing bounded bilinear maps defined on order continuous Banach function spaces

We consider the problem of extending or factorizing a bounded bilinear map defined on a couple of order continuous Banach function spaces to its optimal domain, i.e. the biggest couple of Banach function spaces to which the bilinear map can be extended. As in the case of linear operators, we use vec...

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Detalles Bibliográficos
Autores: Calabuig, J. M.|||0000-0001-8398-8664, Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154, Fernandez Unzueta, M., Galaz Fontes, F.
Tipo de recurso: artículo
Fecha de publicación:2014
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:10251/61397
Acceso en línea:https://riunet.upv.es/handle/10251/61397
Access Level:acceso abierto
Palabra clave:Order continuous
Banach function spaces
Vector measures
Integrable functions
Optimal domain
Bilinear map
MATEMATICA APLICADA
Descripción
Sumario:We consider the problem of extending or factorizing a bounded bilinear map defined on a couple of order continuous Banach function spaces to its optimal domain, i.e. the biggest couple of Banach function spaces to which the bilinear map can be extended. As in the case of linear operators, we use vector measure techniques to find this space, and we show that this procedure cannot be always successfully used for bilinear maps. We also present some applications to find optimal factorizations of linear operators between Banach function spaces.

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