Contents
Introduction vi i
Chapter 0. Preliminary Results and Background 1
a. General notatio n 1
b. An introductio n t o tenso r products . The approximatio n property .
Nuclear operators 2
c. Loca l reflexivity 6
Chapter 1. Absolutely Summing Operators and Basic Applications 9
a. Absolutely summin g operators 9
b. Applications to Banach spaces 16
c. An introduction t o duality theory. Integral operators 18
Notes and reference s 19
Chapter 2. Factorization through a Hilbert Space 2 1
a. Operators factorin g throug h a Hilbert space 2 1
b. A duality theore m 2 5
Notes and reference s 3 0
Chapter 3. Type and Cotype. Kwapieh's Theorem 3 1
a. Type and cotype . Definitions 3 1
b. Kwapieh's theore m 3 2
c. Supplementar y result s 3 4
d. Type and cotyp e and th e geometry of Banach spaces 3 8
Notes and reference s 4 0
Chapter 4. The "Abstract" Version of Grothendieck's Theorem 4 1
a. The factorization theore m 4
b. An applicatio n t o harmonic analysis 4 9
Notes and reference s 5
v
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