Preface to the Second Edition
Preface to the First Edition
Acknowledgments
Symbols and Notation
1 Banach Spaces
1 The Banach Space of Continuous Functions
2 Abstract Banach Spaces
3 The Conjugate Space of Continuous Linear Functionals
4 Examples of Banach spaces: co， l， and l
5 Weak Topologies on Banach Spaces
6 The Alaoglu Theorem
7 The Hahn-Banach Theorem
8 The Conjugate Space of C([0， 1])
9 The Open Mapping Theorem
10 The Lebesgue Spaces: Ll and L
11 The Hardy Spaces: Hl and H
Notes
Exercises
2 Banach Algebras
1 The Banach Algebra of Continuous Functions
2 Abstract Banach Algebras
3 Abstract Index in a banach Algebra
4 The Space of Multiplicative Linear Functions
5 The Gelfand Transform
6 The Gelfand-Mazur Theorem
7 The Gelfand Theorem for Commutative Banach Algebras
8 The Spectral Radius Formula
9 The Stone-Weierstrass Theorem
10 The Generalized Stone-Weierstrass Theorem
11 The Disk Algebra
12 The Algebra of Functions with Absolutey Convergent Fourier series
13 the Algebra of Bounded Measurable Functions
Notes
exercises
3 Geometry of Hilbert Space
……
4 Operators on Hilbert Space and C*-Algebras
5 Compact Operators,Fredholm Operators,and Index Theory
6 The Hardy Spaces
7 Toeplitz Operators
References
Index
