| Descript |
2 volumes : illustrations ; 24 cm |
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text txt rdacontent |
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unmediated n rdamedia |
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volume nc rdacarrier |
| Series |
Cambridge studies in advanced mathematics, 0950-6330 ; 166-167
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Cambridge studies in advanced mathematics ; 166-167
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| Note |
"First published in English by Cambridge University Press 2018"--Title page verso |
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Includes bibliographical references and indexes |
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"This two-volume text provides a complete overview of the theory of Banach spaces, emphasizing its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. The authors give a full exposition of all results, as well as numerous exercises and comments to complement the text and aid graduate students in functional analysis. The book will also be an invaluable reference volume for researchers in analysis. Volume 1 covers the basics of Banach space theory, operatory theory in Banach spaces, harmonic analysis and probability. The authors also provide an annex devoted to compact Abelian groups. Volume 2 focuses on applications of the tools presented in the first volume, including Dvoretzky's theorem, spaces without the approximation property, Gaussian processes, and more. Four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition."-- Provided by publisher |
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V. 1 Preface; Preliminary chapter; 1. Fundamental notions of probability; 2. Bases in Banach spaces; 3. Unconditional convergence; 4. Banach space valued random variables; 5. Type and cotype of Banach spaces. Factorisation through a Hilbert space; 6. p-summing operators. Applications; 7. Some properties of Lp-spaces; 8. The space l1; Annex. Banach algebras, compact Abelian groups; Bibliography; Author index; Notation index; Subject index |
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v. 2 Preface; 1. Euclidean sections; 2. Separable Banach spaces without the approximation property; 3. Gaussian processes; 4. Reflexive subspaces of L1; 5. The method of selectors. Examples of its use; 6. The Pisier space of almost surely continuous functions. Applications; Appendix. News in the theory of infinite-dimensional Banach spaces in the past twenty years G. Godefroy; An update on some problems in high dimensional convex geometry and related probabilistic results O. Gu⥤on; A few updates and pointers G. Pisier; On the mesh condition for Sidon sets L. Rodriguez-Piazza; Bibliography; Author index; Notation index; Subject index |
| Subject |
Banach spaces
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Functional analysis
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Probabilities
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Measure theory
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Probability measures -- Problems, exercises, etc
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Numerical analysis
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Probability measures. fast (OCoLC)fst01077757
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Probabilities. fast (OCoLC)fst01077737
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Numerical analysis. fast (OCoLC)fst01041273
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Measure theory. fast (OCoLC)fst01013175
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Functional analysis. fast (OCoLC)fst00936061
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Banach spaces. fast (OCoLC)fst00826389
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Problems and exercises. fast (OCoLC)fst01423783
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