线性算子的分解和Banach空间的几何

《线性算子的分解和Banach空间的几何（影印版）》综述了Banach空间理论取得的相当大的进展，这是Grothendieck的奠基性论文《拓扑张量积的度量理论概述》的结果。
《线性算子的分解和Banach空间的几何（影印版）》作者考虑的中心问题是Banach空间X和y具有性质：每个从X到y的有界算子都具有Hilbert空间分解，特别是当这些算子定义在Banach格、C*-代数或圆盘代数以及H∞-上时。作者回顾了Grothendieck论文最后提出的六个问题——这些问题现在都已经解决了（除了Grothendieck常数的确切值），这其中包含了这些问题解决过程中的各种结果。在最后一章，作者构造了几个Banach空间，使得内射张量积和射影张量积重合，这给了Grothendieck第六问题一个否定的解决方案。
尽管《线性算子的分解和Banach空间的几何（影印版）》的读者对象是从事泛函分析、调和分析和算子代数等领域研究的数学家，但其详细和完备的处理使具有泛函分析基础的普通读者也能够阅读。事实上，作者特别关注的是近来对Banach空间几何的研究成果，特别是它们如何应用于如调和分析和C*-代数的其他领域。

Introduction
Chapter 0.Preliminary Results and Background
a.General notation
b.An introduction to tensor products.The approximation property.Nuclear operators
c.Local reflexivity
Chapter 1.Absolutely Summing Operators and Basic Applications
a.Absolutely summing operators
b.Applications to Banach spaces
c.An introduction to duality theory.Integral operators
Notes and references
Chapter 2.Factorization through a Hilbert Space
a.Operators factoring through a Hilbert space
b.A duality theorem
Notes and references
Chapter 3.Type and Cotype.Kwapien's Theorem
a.Type and cotype.Definitions
b.Kwapieh's theorem
c.Supplementary results
d.Type and cotype and the geometry of Banach spaces
Notes and references
Chapter 4.The "Abstract" Version of Grothendieck's Theorem
a.The factorization theorem
b.An application to harmonic analysis
Notes and references
Chapter 8.Banach Lattices
a.The Banach lattice version of G.T.
b.Uitraproducts.Factorization through an Lp-space
c.Local unconditional structure. The Gordon-Lewis property
d.Examples of Banach spaces without lu.st.
e.Finite-dimensional spaces with extreme l.u.st.constants
f.G.T.spaces with unconditional basis
g.Infinite-dimensional Kasin decompositions
Notes and references
Chapter 9.C*-Algebras
a.The noncommutative version of G.T.
b.Applications
Notes and references
Chapter 10.Counterexamples to Grothendieck's Conjecture
a.Outline of the construction
b.Extensions of a Banach space
c.The construction
d.Particular cases of the conjectures
e.Some open problems
Notes and references
References