Positively norming sets in Banach function spaces

The notion of positively norming set, a specific definition of norming type sets for Banach lattices, is analyzed. We show that the size of positively norming sets (in terms of compactness and order boundedness) is directly related to the existence of lattice copies of L-1-spaces. As an application,...

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Detalles Bibliográficos
Autores: Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154, Tradacete Pérez, Pedro
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:10251/55476
Acceso en línea:https://riunet.upv.es/handle/10251/55476
Access Level:acceso abierto
Palabra clave:Lattices
Operators
Noncompactness
Boundaries
Theorem
MATEMATICA APLICADA
Descripción
Sumario:The notion of positively norming set, a specific definition of norming type sets for Banach lattices, is analyzed. We show that the size of positively norming sets (in terms of compactness and order boundedness) is directly related to the existence of lattice copies of L-1-spaces. As an application, we provide a version of Kadec-Pelczynski's dichotomy for order continuous Banach function spaces. A general description of positively norming sets using vector measure integration is also given.