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Fundamentos del análisis funcional

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dc.contributor.authorAduén Muskus, Hugo
dc.contributor.authorHerrón Osorio, Sigifredo
dc.date.accessioned2025-08-29T20:32:47Z
dc.date.available2025-08-29T20:32:47Z
dc.date.issued2025-08-29
dc.description.abstractEste libro está dirigido principalmente a estudiantes de pregrado y se espera que el lector tenga conocimiento de la teoría de conjuntos, principalmente de cardinalidad y, además, de algunos tópicos relacionados con espacios métricos y análisis real.
dc.description.editionPrimera edición
dc.description.tableofcontentsIntroducción............ iv
dc.description.tableofcontents1. Espacios vectoriales 1
dc.description.tableofcontents1.1. Definición de campo y valuaciones . . . . . . . . . . . . . . . . 1
dc.description.tableofcontents1.2. Definición de espacio vectorial y ejemplos . . . . . . . . . . . . 9
dc.description.tableofcontents1.3. Bases de Hamel y dimensión . . . . . . . . . . . . . . . . . . . . 27
dc.description.tableofcontents1.4. Operadores Lineales . . . . . . . . . . . . . . . . . . . . . . . . 47
dc.description.tableofcontents1.5. Funcionales lineales . . . . . . . . . . . . . . . . . . . . . . . . . 59
dc.description.tableofcontents1.6. El teorema de Hahn-Banach en espacios lineales . . . . . . . . . 67
dc.description.tableofcontents2. Espacios normados 82
dc.description.tableofcontents2.1. Definiciones y ejemplos . . . . . . . . . . . . . . . . . . . . . . . 82
dc.description.tableofcontents2.2. Espacios de Banach y ejemplos . . . . . . . . . . . . . . . . . . 91
dc.description.tableofcontents2.3. Completación de un espacio normado . . . . . . . . . . . . . . . 114
dc.description.tableofcontents2.4. Espacios normados de dimensión finita . . . . . . . . . . . . . . 118
dc.description.tableofcontents2.5. El Teorema de Baire . . . . . . . . . . . . . . . . . . . . . . . . 130
dc.description.tableofcontents2.6. Bases de Schauder y separabilidad . . . . . . . . . . . . . . . . 137
dc.description.tableofcontents3. Operadores lineales acotados 147
dc.description.tableofcontents3.1. Definiciones, propiedades y ejemplos . . . . . . . . . . . . . . . 147
dc.description.tableofcontents3.2. Operadores invertibles . . . . . . . . . . . . . . . . . . . . . . . 162
dc.description.tableofcontents3.3. Funcionales lineales acotados . . . . . . . . . . . . . . . . . . . 166
dc.description.tableofcontents3.4. El teorema de Hahn-Banach en espacios normados . . . . . . . 186
dc.description.tableofcontents3.5. Dualidad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
dc.description.tableofcontents3.6. Espacios reflexivos . . . . . . . . . . . . . . . . . . . . . . . . . 213
dc.description.tableofcontents3.7. El operador adjunto . . . . . . . . . . . . . . . . . . . . . . . . 220
dc.description.tableofcontents4. Teoremas fundamentales 224
dc.description.tableofcontents4.1. Teorema de Banach–Steinhaus . . . . . . . . . . . . . . . . . . 225
dc.description.tableofcontents4.2. Teorema de la aplicación abierta . . . . . . . . . . . . . . . . . 232
dc.description.tableofcontents4.3. Teorema de la gráfica cerrada . . . . . . . . . . . . . . . . . . . 238
dc.description.tableofcontents4.4. Teorema de normas equivalentes implica TBS . . . . . . . . . . 247
dc.description.tableofcontents5. Espacios de Hilbert 250
dc.description.tableofcontents5.1. Espacios prehilbertiano y espacios de Hilbert . . . . . . . . . . 251
dc.description.tableofcontents5.2. Ortogonalidad . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
dc.description.tableofcontents5.3. Teorema de la distancia mínima . . . . . . . . . . . . . . . . . . 270
dc.description.tableofcontents5.4. Teorema de representación de Riesz . . . . . . . . . . . . . . . 280
dc.description.tableofcontents5.5. Sumas no ordenadas . . . . . . . . . . . . . . . . . . . . . . . . 288
dc.description.tableofcontents5.6. Conjuntos Ortonormales Completos . . . . . . . . . . . . . . . 299
dc.description.tableofcontents5.7. Adjunto de operador lineal acotado en un Hilbert . . . . . . . . 303
dc.description.tableofcontents5.8. Operadores autoadjunto, unitario y normal . . . . . . . . . . . 308
dc.description.tableofcontentsBibliografía....... 314
dc.description.tableofcontentsÍndice alfabético........... 323
dc.format.mimetypeapplication/pdf
dc.identifier.eisbn978-628-7808-08-9
dc.identifier.instnameUniversidad de Córdoba
dc.identifier.reponameRepositorio Universidad de Córdoba
dc.identifier.repourlhttps://repositorio.unicordoba.edu.co/
dc.identifier.urihttps://repositorio.unicordoba.edu.co/handle/ucordoba/9543
dc.language.isospa
dc.publisherFondo Editorial - Universidad de Córdoba
dc.publisher.placeMontería, Córdoba, Colombia
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dc.subject.lcshAnálisis funcionalspa
dc.subject.lcshAnálisis matemáticospa
dc.titleFundamentos del análisis funcional
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