Introduction to Banach Spaces: Analysis and Probability (Volume 1)

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Download Introduction to Banach Spaces: Analysis and Probability (Volume 1) written by Daniel Li, Herve Queffelec in PDF format. This book is under the category Mathematics and bearing the isbn/isbn13 number 1107160510/9781107160514. You may reffer the table below for additional details of the book.

SKU: 8004d637b623 Category: Tag:

Specifications

book-author

Daniel Li, Herve Queffelec

publisher

Cambridge University Press; Vol I

file-type

PDF

pages

463 pages

language

English

asin

B075V7PF2G

isbn10

1107160510

isbn13

9781107160514


Book Description

Introduction to Banach Spaces: Analysis and Probability; Volume 1; (PDF) provides a complete overview of the theory of Banach spaces; focusing its interplay with classical and harmonic analysis (specifically Sidon sets) and probability. The authors give a full exposition of all results; together with numerous exercises and comments to complement the text and help graduate students in functional analysis. The ebook will also be an invaluable reference volume for researchers in the analysis. Volume 1 includes the basics of Banach space theory; operatory theory in Banach spaces; harmonic analysis; and probability. The authors also give an annex devoted to compact Abelian groups. Volume 2 (not included in this) emphasizes applications of the tools presented in the first volume; including Dvoretzky’s theorem; Gaussian processes; spaces without the approximation property; and more.

NOTE: The product includes the ebook; Introduction to Banach Spaces: Analysis and Probability; Volume 1 in PDF. No access codes are included.

Additional information

book-author

Daniel Li, Herve Queffelec

publisher

Cambridge University Press; Vol I

file-type

PDF

pages

463 pages

language

English

asin

B075V7PF2G

isbn10

1107160510

isbn13

9781107160514

Table of contents


Table of contents :
Contents……Page 8
Contents of Volume 2……Page 11
Preface……Page 14
II Weak and Weak* Topologies……Page 32
III Filters, Ultrafilters. Ordinals……Page 38
IV Exercises……Page 43
I Introduction……Page 44
II Convergence……Page 46
III Series of Independent Random Variables……Page 52
IV Khintchine’s Inequalities……Page 61
V Martingales……Page 66
VI Comments……Page 73
VII Exercises……Page 74
II Schauder Bases: Generalities……Page 77
III Bases and the Structure of Banach Spaces……Page 90
IV Comments……Page 105
V Exercises……Page 107
II Unconditional Convergence……Page 114
III Unconditional Bases……Page 121
IV The Canonical Basis of c0……Page 125
V The James Theorems……Page 127
VI The Gowers Dichotomy Theorem……Page 132
VII Comments……Page 141
VIII Exercises……Page 142
II Definitions. Convergence……Page 148
III The Paul Lévy Symmetry Principle and Applications……Page 160
IV The Contraction Principle……Page 164
V The Kahane Inequalities……Page 169
VI Comments……Page 182
VII Exercises……Page 183
II Complements of Probability……Page 190
III Complements on Banach Spaces……Page 203
IV Type and Cotype of Banach Spaces……Page 208
V Factorization through a Hilbert Space and Kwapie´ n’s Theorem……Page 224
VI Some Applications of the Notions of Type and Cotype……Page 231
VII Comments……Page 234
VIII Exercises……Page 236
I Introduction……Page 241
II p-Summing Operators……Page 242
III Grothendieck’s Theorem……Page 248
IV Some Applications of p-Summing Operators……Page 258
V Sidon Sets……Page 262
VI Comments……Page 289
VII Exercises……Page 291
I Introduction……Page 297
II The Space L1……Page 298
III The Trigonometric System……Page 308
IV The Haar Basis in Lp……Page 315
V Another Proof of Grothendieck’s Theorem……Page 327
VI Comments……Page 336
VII Exercises……Page 346
II Rosenthal’s ℓ1 Theorem……Page 357
III Further Results on Spaces Containing ℓ1……Page 372
IV Comments……Page 381
V Exercises……Page 384
II Banach Algebras……Page 388
III Compact Abelian Groups……Page 395
References……Page 413
Notation Index for Volume 1……Page 444
Author Index for Volume 1……Page 446
Subject Index for Volume 1……Page 450
Notation Index for Volume 2……Page 456
Author Index for Volume 2……Page 457
Subject Index for Volume 2……Page 460

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