CONTENTS
Preface 1
0. Preliminarie s 3
0.1. L
p(/j)-spaces
an d 0(5')-space s 3
0.11. Classica l space s of analyti c function s an d the Hilber t transform . . 4
O.III. Absolutel y summin g operators and their relative s 7
1. Th e F . and M . Riesz Theorem and Duals of th e Dis c Algebr a 10
2. Absolutel y Summin g Operators fro m the Dis c Algebr a 13
3. Absolutel y Summin g Operators from the Dis c Algebr a int o Hilber t Space . 19
4. Th e Nonexistenc e o f Loca l Unconditiona l Structur e fo r th e Dis c Algebr a
and for it s Duals 2 4
5. Applicatio n t o Unifor m Algebra s 2 8
6. Uniforml y Peakin g Familie s of Function s i n A an d H°°. Th e Havi n Lemma . 3 6
7. Characterization s o f Weakl y Compac t Set s in L l/HQ an d i n A* 4 3
8. Weakl y Compac t Operator s from A, L xIHX0 an d A* an d Complemente d
Subspaces of Thes e Space s 5 0
9. Complementatio n o f Finit e Dimensiona l Subspaces i n A, L 1 IH1Q an d H°°. 5 6
10. Base s and th e Approximatio n Propert y in Som e Space s of Analyti c Func -
tions
r
6 5
11. Th e Polydis c Algebr a and th e w-Ball Algebra, and Thei r Dual s 7 1
References 8 5
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