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Introduction to Operator Space Theory 1st edition by Gilles Pisier 9780521811651 0521811651

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Author(s): Gilles Pisier
ISBN(s): 9780521811651, 0521811651
Edition: Text is Free of Markings
File Details: PDF, 26.66 MB
Year: 2003
Language: english
SKU: EB-2479422 Category: Tag:

Introduction to Operator Space Theory 1st edition by Gilles Pisier – Ebook PDF Instant Download/Delivery: 9780521811651, 0521811651

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Product details:

ISBN 10: 0521811651

ISBN 13: 9780521811651

Author: Gilles Pisier

The first part of this book is an introduction with emphasis on examples that illustrate the theory of operator spaces. The second part is devoted to applications to C*-algebras, with a systematic exposition of tensor products of C* algebras. The third part of the book describes applications to non self-adjoint operator algebras and similarity problems. The author’s counterexample to the “Halmos problem” is presented, along with work on the new concept of “length” of an operator algebra.

Table of contents:

Part I – Introduction to Operator Spaces

  1. Completely bounded maps

  2. The minimal tensor product. Ruan’s theorem. Basic operations

  3. Minimal and maximal operator space structures

  4. Projective tensor product

  5. The Haagerup tensor product

  6. Characterizations of operator algebras

  7. The operator Hilbert space

  8. Group C*-algebras. Universal algebras and unitization for an operator space

  9. Examples and comments

  10. Comparisons

Part II – Operator Spaces and C-Tensor Products*

  1. C*-norms on tensor products. Decomposable maps. Nuclearity

  2. Nuclearity and approximation properties

  3. C*(F∞) ⊗ B(H)

  4. Kirchberg’s theorem on decomposable maps

  5. The Weak Expectation Property (WEP)

  6. The Local Lifting Property (LLP)

  7. Exactness

  8. Local reflexivity

  9. Grothendieck’s theorem for operator spaces

  10. Estimating the norms of sums of unitaries: Ramanujan graphs, property T, random matrices

  11. Local theory of operator spaces. Nonseparability of OSₙ

  12. B(H) ⊗ B(H)

  13. Completely isomorphic C*-algebras

  14. Injective and projective operator spaces

Part III – Operator Spaces and Non-Self-Adjoint Operator Algebras

  1. Maximal tensor products and free products of operator algebras

  2. The Blecher-Paulsen factorization. Infinite Haagerup tensor products

  3. Similarity problems

  4. The Sz.-Nagy–Halmos similarity problem

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Tags: Gilles Pisier, Introduction, Operator, Space