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出版时间:2020-04

出版社:高等教育出版社

以下为《线性算子分解和Banach空间的几何(影印版)》的配套数字资源,这些资源在您购买图书后将免费附送给您:
  • 高等教育出版社
  • 9787040535037
  • 1版
  • 296646
  • 45245735-1
  • 精装
  • 16开
  • 2020-04
  • 270
  • 172
  • 理学
  • 数学
  • 数学类
  • 研究生(硕士、EMBA、MBA、MPA、博士)
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 .
  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