Some compactness criteria in locally convex and banach spaces

Chapter 1 We study different classes of compact sets. In particular, the class of convex-compact sets is analyzed in depth. Using these classes of sets, we provide compactness criteria by checking on a quite relaxed set of conditions. In order to ensure that we are really dealing with more general n...

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Detalles Bibliográficos
Autor: Monterde Pérez, Ignacio
Tipo de recurso: tesis doctoral
Fecha de publicación:2009
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:10251/14569
Acceso en línea:https://riunet.upv.es/handle/10251/14569
Access Level:acceso abierto
Palabra clave:Compacidad
Espacios de banach
Espacios localmente convexos
Discos de banach
Propiedad drop
MATEMATICA APLICADA
120203 - Algebras y espacios de Banach
120225 - Espacios lineales topológicos
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oai_identifier_str oai:riunet.upv.es:10251/14569
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spelling Some compactness criteria in locally convex and banach spacesMonterde Pérez, IgnacioCompacidadEspacios de banachEspacios localmente convexosDiscos de banachPropiedad dropMATEMATICA APLICADA120203 - Algebras y espacios de Banach120225 - Espacios lineales topológicosChapter 1 We study different classes of compact sets. In particular, the class of convex-compact sets is analyzed in depth. Using these classes of sets, we provide compactness criteria by checking on a quite relaxed set of conditions. In order to ensure that we are really dealing with more general notions, we pay attention to separate the classes introduced. We also provide some stability results of the classes of compact sets used. Some Valdivia and Orihuela theorems are pushed further and an extension of a theorem due to Howard is provided. Chapter 2 We formulate some results on Banach disks and prove that every convex, relatively convex-compact subset of a locally convex space is contained in a Banach disk. We study in which cases some properties, such as separability and reflexivity, are preserved by passing to the generated Banach space. Chapter 3 The drop property, the property (alpha) and the condition (beta) are analyzed. A single technique provides short proofs of some results about drop properties on locally convex spaces. It is shown that the quasi-drop property is equivalent to a drop property for countably closed sets. We prove that the drop and quasi-drop properties, the property (alpha) and the condition (beta) are separably determined. We also study the relation between drop property, property (alpha), condition (beta), compactness and reflexivity.Universitat Politècnica de ValènciaMontesinos Santalucia, VicenteRepositorio Institucional de la Universitat Politècnica de València Riunet20122012-01-2720092009-06-27doctoral thesishttp://purl.org/coar/resource_type/c_db06AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/doctoralThesisapplication/pdftext/plaintext/plaintext/plainapplication/pdfhttps://riunet.upv.es/handle/10251/14569reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/145692026-06-13T07:49:27Z
dc.title.none.fl_str_mv Some compactness criteria in locally convex and banach spaces
title Some compactness criteria in locally convex and banach spaces
spellingShingle Some compactness criteria in locally convex and banach spaces
Monterde Pérez, Ignacio
Compacidad
Espacios de banach
Espacios localmente convexos
Discos de banach
Propiedad drop
MATEMATICA APLICADA
120203 - Algebras y espacios de Banach
120225 - Espacios lineales topológicos
title_short Some compactness criteria in locally convex and banach spaces
title_full Some compactness criteria in locally convex and banach spaces
title_fullStr Some compactness criteria in locally convex and banach spaces
title_full_unstemmed Some compactness criteria in locally convex and banach spaces
title_sort Some compactness criteria in locally convex and banach spaces
dc.creator.none.fl_str_mv Monterde Pérez, Ignacio
author Monterde Pérez, Ignacio
author_facet Monterde Pérez, Ignacio
author_role author
dc.contributor.none.fl_str_mv Montesinos Santalucia, Vicente
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Compacidad
Espacios de banach
Espacios localmente convexos
Discos de banach
Propiedad drop
MATEMATICA APLICADA
120203 - Algebras y espacios de Banach
120225 - Espacios lineales topológicos
topic Compacidad
Espacios de banach
Espacios localmente convexos
Discos de banach
Propiedad drop
MATEMATICA APLICADA
120203 - Algebras y espacios de Banach
120225 - Espacios lineales topológicos
description Chapter 1 We study different classes of compact sets. In particular, the class of convex-compact sets is analyzed in depth. Using these classes of sets, we provide compactness criteria by checking on a quite relaxed set of conditions. In order to ensure that we are really dealing with more general notions, we pay attention to separate the classes introduced. We also provide some stability results of the classes of compact sets used. Some Valdivia and Orihuela theorems are pushed further and an extension of a theorem due to Howard is provided. Chapter 2 We formulate some results on Banach disks and prove that every convex, relatively convex-compact subset of a locally convex space is contained in a Banach disk. We study in which cases some properties, such as separability and reflexivity, are preserved by passing to the generated Banach space. Chapter 3 The drop property, the property (alpha) and the condition (beta) are analyzed. A single technique provides short proofs of some results about drop properties on locally convex spaces. It is shown that the quasi-drop property is equivalent to a drop property for countably closed sets. We prove that the drop and quasi-drop properties, the property (alpha) and the condition (beta) are separably determined. We also study the relation between drop property, property (alpha), condition (beta), compactness and reflexivity.
publishDate 2009
dc.date.none.fl_str_mv 2009
2009-06-27
2012
2012-01-27
dc.type.none.fl_str_mv doctoral thesis
http://purl.org/coar/resource_type/c_db06
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/14569
url https://riunet.upv.es/handle/10251/14569
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
text/plain
text/plain
text/plain
application/pdf
dc.publisher.none.fl_str_mv Universitat Politècnica de València
publisher.none.fl_str_mv Universitat Politècnica de València
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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