经典巴拿赫空间 1和2PDF电子书下载

1．Schauder Bases 1

a．Existence of Bases and Examples 1

b．Schauder Bases and Duality 7

c．Unconditional Bases 15

d．Examples of Spaces Without an Unconditional Basis 24

e．The Approximation Property 29

f．Biorthogonal Systems 42

g．Schauder Decompositions 47

2．The Spaces co and lp 53

a．Projections in co and lp and Characterizations of these Spaces 53

b．Absolutely Summing Operators and Uniqueness of Unconditional Bases 63

c．Fredholm Operators,Strictly Singular Operators and Complemented Subspaces of lp？lr 75

d．Subspaces of co and lp and the Approximation Property,Complement-ably Universal Spaces 84

e．Banach Spaces Containing lp or co 95

f．Extension and Lifting Properties,Automorphisms of l∞,co and l1 104

3．Symmetric Bases 113

a．Properties of Symmetric Bases,Examples and Special Block Bases 113

b．Subspaces of Spaces with a Symmetric Basis 123

4．Orlicz Sequence Spaces 137

a．Subspaces of Orlicz Sequence Spaces which have a Symmetric Basis 137

b．Duality and Complemented Subspaces 147

c．Examples of Orlicz Sequence Spaces 156

d．Modular Sequence Spaces and Subspaces of lp ？lr 166

e．Lorentz Sequence Spaces 175

References 180

Subject Index 185