线性算子分解和Banach空间的几何(影印版)
作者: Gilles Pisier
出版时间:2020-04
出版社:高等教育出版社
- 高等教育出版社
- 9787040535037
- 1版
- 296646
- 46253892-7
- 精装
- 16开
- 2020-04
- 270
- 172
- 理学
- 数学
- 数学类
- 研究生及以上
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 .
e. Finite-dimensional spaces with extreme . 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