本书是Springer数学经典教材之一。本书延续了该系列书的一贯风格,深入但不深沉。材料新颖,许多内容是同类书籍不具备的。对于学习Banach空间结构理论的学者来说,这是一本参考价值极高的书籍;对于学习该科目的读者,本书也是同等重要。
1.Schauder Bases
a.Existence of Bases and Examples
b.Schauder Bases and Duality
c.Unconditional Bases
d.Examples of Spaces Without an Unconditional Basis
e.The Approximation Property
f.Biorthogonal Systems
g.Schauder Decompositions
2.The Spaces co and lp
a.Projections in co and lp and Characterizations of these Spaces
b.Absolutely Summing Operators and Uniqueness of Unconditional Bases
c.Fredholm Operators, Strictly Singular Operators and Complemented Subspaces of lp lr
d.Subspaces of Co and lp and the Approximation Property, Complementably Universal Spaces
e.Banach Spaces Containing lp or c0
f.Extension and Lifting Properties, Automorphisms of l∞, c0 and l1
3.Symmetric Bases
a.Properties of Symmetric Bases, Examples and Special Block Bases
b.Subspaces of Spaces with a Symmetric Basis
4.Orlicz Sequence Spaces
a.Subspaces of Orlicz Sequence Spaces which have a Symmetric Basis
b.Duality and Complemented Subspaces
c.Examples of Orlicz Sequence Spaces
d.Modular Sequence Spaces and Subspaces of lp lr
e.Lorentz Sequence Spaces
References
Subject Index