线性算子分解和Banach空间的几何（影印版）

样章

作者：

Gilles Pisier

定价：

99.00 元

版面字数：

270千字

开本：

16开

装帧形式：

精装

版次：

最新版次
印刷时间：

2020年

ISBN：

978-7-04-053503-7

物料号：

53503-00

出版时间：

2020-04-22

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

代数几何学

暂无

目录
- 前辅文
- 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. Kwapieh'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 5. Grothendieck's Theorem
  - a. Preliminaries. Localization techniques. J^-spaces
  - b. Operators on C( K )-spaces
  - c. Operators on Lj-spaces
  - d. Cotype 2 spaces and absolutely summing operators
  - e. Best constants. Krivine's proof
  - f. A proof of G.T. using harmonic analysis
  - Notes and references
- Chapter 6. Banach Spaces Satisfying Grothendieck's Theorem
  - a. G.T. spaces
  - b. G.T. spaces of cotype 2
  - c. Quotients of Ll by a reflexive subspace
  - d. Bourgain's theorem on Lx/Hl
  - Notes and references
- Chapter 7. Applications of the Volume Ratio Method
  - Notes and references
- Chapter 8. Banach Lattices
  - a. The Banach lattice version of G.T.
  - b. Ultraproducts. Factorization through an L^-space
  - c. Local unconditional structure. The Gordon-Lewis property
  - d. Examples of Banach spaces without l.u.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