iv CONTENTS
Chapter 8. Integrability 43
8.1. Integrability of Φ 43
8.2. Integrability of Φ b Φ 44
8.3. Integrability of the inner product 48
Chapter 9. A Parseval-like formula for xx, yy, x P
lp,
y P
lq
51
Chapter 10. Grothendieck-like theorems in dimensions ą 2? 57
10.1. A multidimensional version of Question 2.3 57
10.2. A multidimensional version of Question 2.6 58
Chapter 11. Fractional Cartesian products and multilinear functionals on a
Hilbert space 61
11.1. Projective boundedness and projective continuity 61
11.2. Fractional Cartesian products 64
11.3. A characterization of projectively continuous functionals 68
Chapter 12. Proof of Theorem 11.11 73
12.1. A multilinear Parseval-like formula 73
12.2. The left-side inequality in (11.81) 82
12.3. The right-side inequality in (11.81) 84
12.4. Multilinear extensions of the Grothendieck inequality 85
Chapter 13. Some loose ends 87
13.1.
˜
V 2pX ˆ Y q vs.
˜
V 2pX ˆ Y q, G2pX ˆ Y q vs. G2pX ˆ Y q 87
13.2. G2pX ˆ Y q
˜
V 2pX ˆ Y q vs. G2pX ˆ Y q
˜
V 2pX ˆ Y q 87
13.3. Projective boundedness vs. projective continuity 87
13.4. A characterization of projective boundedness 88
Bibliography 89
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