Classical Banach spaces I and II

Cover......Page 1
Title page of the reprint edition......Page 3
Copyright page of the reprint edition......Page 4
Title page of Volume I, the 1977 edition......Page 5
Copyright page of Volume I, of the 1977 edition......Page 6
Dedication......Page 7
Preface......Page 9
Table of Contents......Page 12
Standard Definitions, Notations and Conventions......Page 13
a. Existence of Bases and Examples......Page 17
b. Schauder Bases and Duality......Page 23
c. Unconditional Bases......Page 31
d. Examples of Spaces Without an Unconditional Basis......Page 40
e. The Approximation Property......Page 45
f. Biorthogonal Systems......Page 58
g. Schauder Decompositions......Page 63
a. Projections in $c_0$ and $l_p$ and Characterizations of these Spaces......Page 69
b. Absolutely Summing Operators and Uniqueness of Unconditional Bases......Page 79
c. Fredholm Operators, Strictly Singular Operators and Complemented Subspaces of $l_p \\oplus l_r$......Page 91
d. Subspaces of $c_0$ and $l_p$ and the Approximation Property, Complement - ably Universal Spaces......Page 100
e. Banach Spaces Containing $l_p$ or $c_0$......Page 111
f. Extension and Lifting Properties, Automorphisms of $l_\\infty$, $c_0$ and $l_1$......Page 120
a. Properties of Symmetric Bases, Examples and Special Block Bases......Page 129
b. Subspaces of Spaces with a Symmetric Basis......Page 139
a. Subspaces of Orlicz Sequence Spaces which have a Symmetric Basis......Page 153
b. Duality and Complemented Subspaces......Page 163
c. Examples of Orlicz Sequence Spaces......Page 172
d. Modular Sequence Spaces and Subspaces of $l_p \\oplus l_r$......Page 182
e. Lorentz Sequence Spaces......Page 191
References......Page 196
Subject Index......Page 201
Title page of Volume II, the 1979 edition......Page 207
Copyright page of Volume II, of the 1979 edition......Page 208
Dedication......Page 209
Preface......Page 211
Table of Contents......Page 213
a. Basic Definitions and Results......Page 215
b. Concrete Representation of Banach Lattices......Page 228
c. The Structure of Banach Lattices and their Subspaces......Page 245
d. $p$-Convexity in Banach Lattices......Page 254
e. Uniform Convexity in General Banach Spaces and Related Notions......Page 273
f. Uniform Convexity in Banach Lattices and Related Notions......Page 293
g. The Approximation Property and Banach Lattices......Page 316
a. Basic Definitions, Examples and Results......Page 328
b. The Boyd Indices......Page 343
c. The Haar and the Trigonometric Systems......Page 364
d. Some Results on Complemented Subspaces......Page 382
e. Isomorphisms Between r.i. Function Spaces; Uniqueness of the r.i. Structure......Page 395
f. Applications of the Poisson Process to r.i. Function Spaces......Page 416
g. Interpolation Spaces and their Applications......Page 429
References......Page 447
Subject Index......Page 453