Fernando Albiac、Nigel J.Kalton所著的《巴拿赫空间理论讲义》是一部讲述巴拿赫空间的教程。独立性强，只需简单的泛函分析知识即可完全读懂这本书。书中提供了全面了解现代巴拿赫空间理论的观点和技巧，重点强调典型勒贝格空间Lp和连续函数空间；同时也强调了巴拿赫空间同构理论，基和基本序列的应用技巧。这些都旨在为读者提供必需的技巧工具，无需了解许多更多的概念而直达学术前沿。书中包括了许多详尽、容易理解的证明，以及大量例子和练习。

1 Bases and Basic Sequences

 1.1 Schauder bases

 1.2 Examples: Fourier series

 1.3 Equivalence of bases and basic sequences

 1.4 Bases and basic sequences: discussion

 1.5 Constructing basic sequences

 1.6 The Eberlein-Smulian Theorem

 Problems

2 The Classical Sequence Spaces

 2.1 The isomorphic structure of the lp-spaces and co

 2.2 Complemented subspaces of lp (1 ≤ p < ∞) and co

 2.3 The space ll

 2.4 Convergence of series

 2.5 Complementability of co

 Problems

3 Special Types of Bases

 3.1 Unconditional bases

 3.2 Boundedly-complete and shrinking bases

 3.3 Nonreflexive spaces with unconditional bases

 3.4 The James space J

 3.5 A litmus test for unconditional bases

 Problems

4  Banach Spaces of Continuous Functions

 4.1 Basic properties

 4.2 A characterization of real C(K)-spaces

 4.3 Isometrically injective spaces

 4.4 Spaces of continuous functions on uncountable compact

metric spaces

 4.5 Spaces of continuous functions on countable compact metric

spaces

 Problems

5 L1(μ)-Spaces and C(K)-Spaces

 5.1 General remarks about L1 (μ)-spaces

 5.2 Weakly compact subsets of L1 (μ)

 5.3 Weak compactness in M(K)

 5.4 The Dunford-Pettis property

 5.5 Weakly compact operators on C(K)-spaces

 5.6 Subspaces of L1(μ)-spaces and C(K)-spaces

 Problems

6 The Lp-Spaces for 1 ≤ p < oo

 6.1 Conditional expectations and the Haar basis

 6.2 Averaging in Banach spaces

 6.3 Properties of L1

 6.4 Subspaces of Lp

 Problems

7 Pactorization Theory

 7.1 Maurey-Nikishin factorization theorems

 7.2 Subspaces of Lp for 1 ≤ p < 2

 7.3 Factoring through Hilbert spaces

 7.4 The Kwapien-Maurey theorems for type-2 spaces

 Problems ....

8 Absolutely Summing Operators

 8.1 Grothendieck's Inequality

 8.2 Absolutely summing operators

 8.3 Absolutely summing operators on L1(μ)-spaces

 Problems

9  Perfectly Homogeneous Bases and Their Applications

 9.1 Perfectly homogeneous bases

 9.2 Symmetric bases

 9.3 Uniqueness of unconditional basis

 9.4 Complementation of block basic sequences

 9.5 The existence of conditional bases

 9.6 Greedy bases

 Problems

10 lp-Subspaces of Banach Spaces

 10.1 Ramsey theory

 10.2 Rosenthal's l1 theorem

 10.3 Tsirelson space

 Problems

11 Finite Representability of lp-Spaces

 11.1 Finite representability

 11.2 The Principle of Local Reflexivity

 11.3 Krivine's theorem

 Problems

12 An Introduction to Local Theory

 12.1 The John ellipsoid

 12.2 The concentration of measure phenomenon

 12.3 Dvoretzky's theorem

 12.4 The complemented subspace problem

 Problems

13 Important Examples of Banach Spaces

 13.1 A generalization of the James space

 13.2 Constructing Banach spaces via trees

 13.3 Petczynski's universal basis space

 13.4 The James tree space

A Fundamental Notions

B Elementary Hilbert Space Theory

C Main Features of Finite-Dimensional Spaces

D Cornerstone Theorems of Functional Analysis

 D.1 The Hahn-Banach Theorem

 D.2 Baire's Theorem and its consequences

E Convex Sets and Extreme Points

F The Weak Topologies

G Weak Compactness of Sets and Operators

List of Symbols

References

Index