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Author Li, Daniel, author
Title Introduction to Banach spaces : analysis and probability / Daniel Li, Herve Queffelec
Imprint Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2018
book jacket
 Mathematics Library  QA322.2 L513 2018  v.1    AVAILABLE    30340200558165
 Mathematics Library  QA322.2 L513 2018  v.2    AVAILABLE    30340200558173
Descript 2 volumes : illustrations ; 24 cm
text txt rdacontent
unmediated n rdamedia
volume nc rdacarrier
Series Cambridge studies in advanced mathematics, 0950-6330 ; 166-167
Cambridge studies in advanced mathematics ; 166-167
Note "First published in English by Cambridge University Press 2018"--Title page verso
Includes bibliographical references and indexes
"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
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
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
Functional analysis
Measure theory
Probability measures -- Problems, exercises, etc
Numerical analysis
Probability measures. fast (OCoLC)fst01077757
Probabilities. fast (OCoLC)fst01077737
Numerical analysis. fast (OCoLC)fst01041273
Measure theory. fast (OCoLC)fst01013175
Functional analysis. fast (OCoLC)fst00936061
Banach spaces. fast (OCoLC)fst00826389
Problems and exercises. fast (OCoLC)fst01423783
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