說明 
2 volumes : illustrations ; 24 cm 

text txt rdacontent 

unmediated n rdamedia 

volume nc rdacarrier 
系列 
Cambridge studies in advanced mathematics, 09506330 ; 166167


Cambridge studies in advanced mathematics ; 166167

附註 
"First published in English by Cambridge University Press 2018"Title page verso 

Includes bibliographical references and indexes 

"This twovolume 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. psumming operators. Applications; 7. Some properties of Lpspaces; 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 infinitedimensional 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. RodriguezPiazza; Bibliography; Author index; Notation index; Subject index 
主題 
Banach spaces


Functional analysis


Probabilities


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

