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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 |
|---|---|
| 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.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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|---|---|---|---|
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| 003 | OCoLC | ||
| 005 | 20231017213018.0 | ||
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| 050 | 4 | |a QA322 | |
| 072 | 7 | |a MAT |x 031000 |2 bisacsh | |
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| 100 | 1 | |a Perez-Garcia, C. | |
| 245 | 1 | 0 | |a Locally Convex Spaces over Non-Archimedean Valued Fields. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2010. | ||
| 300 | |a 1 online resource (488 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Cambridge Studies in Advanced Mathematics, 119 ; |v v. 119 | |
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 500 | |a 9.2 Spaces with an orthogonal'' base. | ||
| 520 | |a A comprehensive, self-contained treatment of non-Archimedean functional analysis, with an emphasis on locally convex space theory. | ||
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references and index. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Locally convex spaces. | |
| 650 | 0 | |a Functional analysis. | |
| 650 | 6 | |a Espaces localement convexes. | |
| 650 | 6 | |a Analyse fonctionnelle. | |
| 650 | 7 | |a MATHEMATICS |x Transformations. |2 bisacsh | |
| 650 | 7 | |a Functional analysis |2 fast | |
| 650 | 7 | |a Locally convex spaces |2 fast | |
| 700 | 1 | |a Schikhof, W. H. | |
| 776 | 0 | 8 | |i Print version: |a Perez-Garcia, C. |t Locally Convex Spaces over Non-Archimedean Valued Fields. |d Cambridge : Cambridge University Press, ©2010 |z 9780521192439 |
| 830 | 0 | |a Cambridge Studies in Advanced Mathematics, 119. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=320362 |z Texto completo |
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