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Introduction to Banach Spaces: Analysis and Probability 2 Volume Hardback Set (Series Numbers 166-167) - Daniel Li, Hervé Queffélec

Introduction to Banach Spaces: Analysis and Probability 2 Volume Hardback Set (Series Numbers 166-167)

Media-Kombination
890 Seiten
2017
Cambridge University Press
978-1-107-16263-1 (ISBN)
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This two-volume text provides a complete overview of the theory of Banach spaces, emphasising its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. Written for graduate students, this text is also a valuable reference volume for researchers in analysis.
This two-volume text provides a complete overview of the theory of Banach spaces, emphasising 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. In volume 2, four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.

Daniel Li is a Professor at Université d'Artois, France. Hervé Queffélec is Emeritus Professor at Université de Lille I. He has published over sixty papers, two research books, and four textbooks, including Twelve Landmarks of Twentieth-Century Analysis (2015).

Volume 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. Volume 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. Guédon; A few updates and pointers G. Pisier; On the mesh condition for Sidon sets L. Rodriguez-Piazza; Bibliography; Author index; Notation index; Subject index.

Erscheint lt. Verlag 2.11.2017
Reihe/Serie Cambridge Studies in Advanced Mathematics
Übersetzer Danièle Gibbons, Greg Gibbons
Zusatzinfo Worked examples or Exercises; 7 Line drawings, black and white
Verlagsort Cambridge
Sprache englisch
Maße 158 x 235 mm
Gewicht 1430 g
Themenwelt Mathematik / Informatik Mathematik Analysis
ISBN-10 1-107-16263-7 / 1107162637
ISBN-13 978-1-107-16263-1 / 9781107162631
Zustand Neuware
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