**CBMS Regional Conference Series in Mathematics**

Volume: 60;
1986;
154 pp;
Softcover

MSC: Primary 47;
Secondary 46

Print ISBN: 978-0-8218-0710-1

Product Code: CBMS/60

List Price: $31.00

Individual Price: $24.80

**Electronic ISBN: 978-1-4704-2421-3
Product Code: CBMS/60.E**

List Price: $31.00

Individual Price: $24.80

# Factorization of Linear Operators and Geometry of Banach Spaces

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*Gilles Pisier*

A co-publication of the AMS and CBMS

This book surveys the considerable progress made in Banach space
theory as a result of Grothendieck's fundamental paper

Although the book is aimed at mathematicians working in functional
analysis, harmonic analysis and operator algebras, its detailed and
self-contained treatment makes the material accessible to nonspecialists with
a grounding in basic functional analysis. In fact,
the author is particularly concerned to develop very recent results in
the geometry of Banach spaces in a form that emphasizes how they may
be applied in other fields, such as harmonic analysis and
\(C^*\)-algebras.

#### Table of Contents

# Table of Contents

## Factorization of Linear Operators and Geometry of Banach Spaces

- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Contents v6 free
- Introduction vii8 free
- Chapter 0. Preliminary Results and Background 112 free
- Chapter 1. Absolutely Summing Operators and Basic Applications 920
- Chapter 2. Factorization through a Hilbert Space 2132
- Chapter 3. Type and Cotype. Kwapieh's Theorem 3142
- Chapter 4. The "Abstract" Version of Grothendieck's Theorem 4152
- Chapter 5. Grothendieck's Theorem 5364
- a. Preliminaries. Localization techniques. L[sub(p)]-spaces 5364
- b. Operators on C( K )-spaces 5465
- c. Operators on L[sub(1)]-spaces 5768
- d. Cotype 2 spaces and absolutely summing operators 6273
- e. Best constants. Krivine's proof 6475
- f. A proof of G.T. using harmonic analysis 6879
- Notes and references 6980

- Chapter 6. Banach Spaces Satisfying Grothendieck's Theorem 7182
- Chapter 7. Applications of the Volume Ratio Method 89100
- Chapter 8. Banach Lattices 97108
- a. The Banach lattice version of G.T. 97108
- b. Ultraproducts. Factorization through an L[sub(p)]-space 101112
- c. Local unconditional structure. The Gordon-Lewis property 104115
- d. Examples of Banach spaces without l.u.st. 108119
- e. Finite-dimensional spaces with extreme l.u.st. constants 113124
- f. G.T. spaces with unconditional basis 114125
- g. Infinite-dimensional Kašin decompositions 114125
- Notes and references 118129

- Chapter 9. C *-Algebras 119130
- Chapter 10. Counterexamples to Grothendieck's Conjecture 135146
- References 149160
- Back Cover Back Cover1166