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Locally Convex Spaces over Non-Archimedean Valued Fields.
A comprehensive, self-contained treatment of non-Archimedean functional analysis, with an emphasis on locally convex space theory.
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2010.
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| Colección: | Cambridge Studies in Advanced Mathematics, 119.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Half-title; Series-title; Title; Copyright; Dedication; Contents; Preface; Aim; History; Foreign affairs; Book organization; 1 Ultrametrics and valuations; 1.1 Ultrametric spaces; 1.2 Ultrametric fields; 1.3 Notes; 2 Normed spaces; 2.1 Basics; 2.2 Orthogonality; 2.3 Spaces of countable type; 2.4 The absence of Hilbert space; 2.5 Examples of Banach spaces; 2.5.1 The space c0(I); 2.5.2 The space ... ; 2.5.3 Banach spaces of continuous functions; C(X) for compact X; The space C0(X) of continuous functions vanishing at infinity; PC(X) and BC(X); 2.5.4 Valued field extensions.
- 2.5.5 Spaces of power series2.5.6 Analytic elements; 2.5.7 Cn-functions; 2.6 Notes; 3 Locally convex spaces; 3.1 Seminorms and convexity; 3.2 Absolutely convex sets of countable type; 3.3 Definition of a locally convex space; 3.4 Basic facts and constructions; 3.5 Metrizable and Frechet spaces; 3.6 Bounded sets; 3.7 Examples of locally convex spaces; 3.7.1 Spaces of continuous functions; 3.7.2 Spaces of analytic functions; 3.7.3 Spaces of differentiable functions; 3.8 Compactoids; 3.9 Compactoidity vs orthogonality; 3.10 Characterization of compactoids in normed spaces by means of t-frames.
- 3.11 Notes4 The Hahn-Banach Theorem; 4.1 A first Hahn-Banach Theorem: spherically complete scalar fields; 4.2 A second Hahn-Banach Theorem: spaces of countable type; 4.3 Examples of spaces (strictly) of countable type; 4.4 A third Hahn-Banach Theorem: polar spaces; 4.5 Notes; 5 The weak topology; 5.1 Weak topologies and dual-separating spaces; 5.2 Weakly closed convex sets; 5.3 Weak topologies and spaces of finite type; 5.4 Weakly bounded sets; 5.5 Weakly convergent sequences; 5.6 Weakly (pre)compact sets and orthogonality''; 5.7 Admissible topologies and the Mackey topology; 5.8 Notes.
- 6 C-compactness6.1 Basics; 6.2 Permanence properties; 6.3 Notes; 7 Barrelledness and reflexivity; 7.1 Polar barrelledness, hereditary properties; 7.2 Examples of (polarly) barrelled spaces; 7.2.1 Immediate examples; 7.2.2 Barrelledness of spaces of continuous functions; 7.2.3 Barrelledness of spaces of differentiable functions; 7.3 The weak star and the strong topology on the dual; 7.4 Reflexivity; 7.5 Examples of reflexive spaces; 7.5.1 Reflexivity of Banach spaces; 7.5.2 Reflexivity of locally convex spaces of continuous functions.
- 7.5.3 Reflexivity of locally convex spaces of differentiable functions7.6 Metrizability considerations in duality theory; 7.7 Notes; 8 Montel and nuclear spaces; 8.1 Compactoid operators; 8.2 Intermezzo: a curious property of ... ; 8.3 Compactifying operators; 8.4 (Semi- )Montel spaces; 8.5 Nuclear spaces; 8.6 Semi-Montelness, nuclearity and metrizability; 8.7 Examples of (semi- )Montel and nuclear spaces; 8.7.1 Spaces of continuous functions; 8.7.2 Spaces of differentiable functions; 8.8 Notes; 9 Spaces with an orthogonal'' base; 9.1 Bases in locally convex spaces.