Some linear topological properties of the hardy spaces ${𝐇}^p$

 Access to full text

 Full (PDF)

1. [1] V.M. Adamian, D.Z. Arov and M.G. Krein: On infinite Hankel matrices and generalized problems of Caratheodory-Fejer and F. Riesz. Funkt. Analiz i Prilož., vol. 2, No 1 (1968) 1-19 (Russian). Zbl0174.45203MR234274
2. [2] C. Bessaga and A. Pelczyński: On bases and unconditional convergence of series in Banach spaces. Studia Math.17 (1958) 151-164. Zbl0084.09805MR115069
3. [3] P. Billard: Bases dans H et bases de sous espaces de dimension finie dans A, Linear Operators and approximation. Proc. Conference in Oberwolfach August 14-22 (1971) Edited by P. L. Butzer, J.-P. Kahane and B. Sz.-Nagy, Birkhäuser Verlag, Basel und Stuttgart (1972) 310-324. Zbl0261.46019MR428013
4. [4] R.P. Boas: Isomorphism between Hp and Lp. Amer. J. Math.,77 (1955) 655-656. Zbl0065.34502MR77704
5. [5] D. Dacunha-Castelle et L. Krivine: Sous-Espaces de L1. Universite Paris XI. Preprint No 142 (1975). Zbl0295.46046
6. [6] E. Dubinsky, A. Pelczyński and H.P. Rosenthal: On Banach spaces for which Π2(Lα, X) = B(L∞, X). Studia Math.44 (1972) 617-648. Zbl0262.46018
7. [7] P.L. Duran: Theory of Hp spaces. Academic Press, New York and London1970. Zbl0215.20203
8. [8] P.L. Duren, B.W. Romberg and A.L. Shields: Linear functionals on Hp spaces with 0 < p < 1. J. Reine Angew. Math.238 (1969) 32-60. Zbl0176.43102MR259579
9. [9] G. Bennet, L.E. Dor, V. Goodman, W.B. Johnson and C.M. Newman: On uncomplemented subspaces of Lp(1 < p < 2). Israel J. Math. (to appear). Zbl0339.46022MR435822
10. [10] Y. Gordon and D.R. Lewis: Absolutely summing operators and local unconditional structures. Acta Math.133 (1974) 27-47. Zbl0291.47017MR410341
11. [11] Y. Gordon, D.R. Lewis and J.R. Retherford: Banach ideals of operators with applications. J. Functional Analysis14 (1973) 295-306. Zbl0272.47024MR380488
12. [12] A. Grothendieck: Résumé de la théorie métrique des produits tensoriels topologiques. Bol. Soc. Matem., Sao Paulo8 (1956) 1-79. Zbl0074.32303MR94682
13. [13] A. Grothendieck: Sur les applications lineares faiblement compactes d'espaces du type C(K). Canadian J. Math.5 (1953) 129-173. Zbl0050.10902MR58866
14. [14] K. Hoffman: Banach spaces of analytic functions. Prentice-Hall, Englewood Cliffs, N.J.1962. Zbl0117.34001MR133008
15. [15] M.I. Kadec and A. Pelczyński: Bases, lacunary sequences and complemented subspaces in the spaces Lp. Studia Math.,21 (1962) 161-176. Zbl0102.32202
16. [16] J. Lindenstrauss and A. Pelczyński: Absolutely summing operators in Lp spaces and their applications. Studia Math.29 (1968) 275-326. Zbl0183.40501MR231188
17. [17] J. Lindenstrauss and A. Pelczyński: Contributions to the theory of the classical Banach spaces. J. Funct. Analysis, 8 (1971) 225-244. Zbl0224.46041MR291772
18. [18] J. Lindenstrauss and H.P. Rosenthal: The Lp spaces. Israel J. Math., 7 (1969) 325-349. Zbl0205.12602MR270119
19. [19] B. Maurey: Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces Lp. Astérisque11 (1974) 1-163. Zbl0278.46028MR344931
20. [20] B. Maurey: Expose No 15, Seminaire Maurey-Schwartz Espaces Lp et applications radonifiantes. Ecole Polytechnique, Paris1972-1973. 
21. [21] R.E.A.C. Paley: On the lacunary coefficients of power series. Ann. of Math., 34 (1933) 615-616. Zbl0007.24401MR1503129JFM59.0302.03
22. [22] A. Pelczyński: Projections in certain Banach spaces. Studia Math., 19 (1960) 209-228. Zbl0104.08503MR126145
23. [23] A. Pelczyński: On the impossibility of embedding of the space L in certain Banach spaces. Coll. Math., 8 (1961) 199-203. Zbl0099.09501MR131154
24. [24] A. Pelczyński: Sur certaines propriétés isomorphiques nouvelles des espaces de Banach de fonctions holomorphes A et H∞. C.R. Acad. Sc. Paris, t. 279 (1974) Série A, 9-12. Zbl0285.46020
25. [25] A. Pelczyński and H.P. Rosenthal: Localization techniques in Lp spaces. Studia Math., 52 (1975) 263-289. Zbl0297.46023MR361729
26. [26] H.P. Rosenthal: Projections onto translation-invariant subspaces of Lp(G). Memoirs AMS63 (1966). Zbl0203.43903MR211198
27. [27] H.P. Rosenthal: On subspaces of Lp. Annals of Math., 97 (1973) 344-373. Zbl0253.46049MR312222
28. [28] H.P. Rosenthal: A characterization of Banach spaces containing l1. Proc. Nat. Acad. Sci. USA, vol. 7 (1974) 2411-2413. Zbl0297.46013MR358307
29. [29] W. Rudin: Remarks on a theorem of Paley. J. London Math. Soc., 32 (1957) 307-311. Zbl0078.05904MR94650
30. [30] W. Rudin: Trigonometric series with gaps. J. Math. Mech., 9 (1960) 203-227. Zbl0091.05802MR116177
31. [31] A.L. Shields and D.L. Williams: Bounded projections, duality, and multipliers in spaces of analytic functions. Trans. Amer. Math. Soc., 162 (1971) 287-302. Zbl0227.46034MR283559
32. [32] Kosaku Yosida: Functional Analysis. Springer Verlag, New York, Heidelberg, Berlin1965. Zbl0435.46002
33. [33] A. Zygmund: Trigonometric series I, II. Cambridge University Press, London and New York1959. Zbl0085.05601MR107776