VI
CONTENTS
Chapter 5. Grothendieck's Theorem 5 3
a. Preliminaries. Localization techniques. J^-spaces 5 3
b. Operators on C( K )-spaces 5 4
c. Operators on Lj-space s 5 7
d. Cotype 2 spaces and absolutely summing operators 6 2
e. Bes t constants. Krivine's proof 6 4
f. A proof o f G.T. using harmonic analysis 6 8
Notes and reference s 6 9
Chapter 6. Banach Spaces Satisfying Grothendieck's Theorem 7 1
a. G.T. spaces 7
b. G.T. spaces of cotype 2 7 3
c. Quotients of L
l
b y a reflexive subspac e 7 8
d. Bourgain's theorem on L
x/Hl
8 3
Notes and reference s 8 6
Chapter 7. Applications of the Volume Ratio Method 8 9
Notes and reference s 9 5
Chapter 8. Banach Lattices 9 7
a. The Banach lattice version of G.T. 9 7
b. Ultraproducts. Factorization throug h an L^-spac e 101
c. Loca l unconditional structure. The Gordon-Lewis property 104
d. Examples of Banach spaces without l.u.st. 108
e. Finite-dimensiona l spaces with extreme l.u.st. constants 113
f. G.T . spaces with unconditional basis 114
g. Infinite-dimensional Kasi n decompositions 114
Notes and reference s 18
Chapter 9. C *-Algebras 19
a. The noncommutative version of G.T. 119
b. Applications 130
Notes and reference s 132
Chapter 10. Counterexamples to Grothendieck's Conjecture 135
a. Outline of the construction 135
b. Extensions of a Banach space 137
c. The construction 140
d. Particular cases of the conjectures 145
e. Some open problems 146
Notes and reference s 147
References 149
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