Chapter 30 Type, cotype and k-convexity

Handbook of the Geometry of Banach Spaces

Volumn 2, Issue , 2003, Pages 1299-1332

  Maurey, Bernard ^a  

^a UFR des Sciences et Technologie   (France)

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EID: 67649622621     PISSN: 18745849     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-5849(03)80037-2     Document Type: Chapter

References (66)

1. Beck A. A convexity condition in Banach spaces the strong law of large numbers. Proc. Amer. Math. Soc. 13 (1962), 329-334
2. Benyamini Y., and Lindenstrauss J. Geometric Nonlinear Functional Analysis. Amer. Math. Soc. Colloq. Publ. 48 (1999)
3. n. Invent. Math. 88 (1987) 319-340
4. Brunel [A., and Sucheston L. On B-convex Banach spaces. Math. Systems Theory 7 (1974) 294-299
5. Brunei A., and Sucheston L. On J-convexity and some ergodic super-properties of Banach spaces. Trans. Amer. Math. Soc. 204 (1975) 79-90
6. Carl B. Inequalities of Bernstein Jackson-type the degree of compactness of operators in Banach spaces. Ann. Inst. Fourier 35 3 (1985) 79-118
7. Dacunha-Castelle D., and Krivine J.L. Applications des ultraproduits à l'étude des espaces et des algèbres de Banach. Studia Math. 41 (1972) 315-334
8. ∞ X). Studia Math. 44 (1972) 617-648
9. erratum, 1554. Dvoretzky A. A theorem on convex bodies applications to Banach spaces. Proc. Nat. Acad. Sci. USA 45 (1959) 223-226
10. (Jerusalem, 1960). Dvoretzky A. Some results on convex bodies and Banach spaces. Proc. Internat. Sympos. Linear Spaces (1961), Jerusalem Academic Press, Jerusalem; Pergamon, Oxford 123-160
11. Dvoretzky A., and Rogers C.A. Absolute and unconditional convergence in normed linear spaces. Proc. Nat. Acad. Sci. USA 36 (1950) 192-197
12. Enflo P. Banach spaces which can be given an equivalent uniformly convex norm. Israel J. Math. 13 (1973) 281-288
13. Figiel T., Lindenstrauss J., and Milman V.D. The dimension of almost spherical sections of convex bodies. Acta Math. 139 (1977) 53-94
14. Figiel T., and Tomczak-Jaegermann N. Projections onto Hilbertian subspaces of Banach spaces. Israel J. Math. 33 (1979) 155-171
15. Giesy D.P. On a convexity condition in normed linear spaces. Trans. Amer. Math. Soc. 125 (1966) 114-146
16. Giesy D.P. B-convexity reflexivity. Israel J. Math. 15 (1973) 430-436
17. (this Handbook). Gowers W.T. Ramsey methods in Banach spaces. In: Johnson W.B., and Lindenstrauss J. (Eds). Handbook of the Geometry of Banach Spaces Vol. 2 (2003), Elsevier, Amsterdam 1071-1097
18. (Berkeley, CA, 1965/66). Gross L. Abstract Wiener spaces. Part 1. Contributions to Probability Theory. Proc. Fifth Berkeley Sympos. Math. Statist, and Probab. Vol. II (1967), Univ. California Press, Berkeley 31-42
19. Gross L. Abstract Wiener measure and infinite dimensional potential theory. Lectures in Modern Analysis and ApplicationsII. Lecture Notes in Math. 140 (1970), Springer, Berlin 84-116
20. Grothendieck A. Resume de la théorie métrique des produits tensoriels topologiques. Bol. Soc. Mat. Sao Paulo 8 (1953) 1-79
21. Haagerup U. The Grothendieck inequality for bilinear forms on C*-algebras. Adv. in Math. 56 (1985) 93-116
22. Hoffman-Jørgensen J. Sums of independent Banach space valued random variables. Studia Math. 52 (1974) 159-186
23. Hoffman-Jørgensen J. The strong law of large numbers and the central limit theorem in Banach spaces. Proceedings of the Seminar on Random Series. Convex Sets and Geometry of Banach Spaces, Various Publications Series No. 24 (1975), Mat. Inst., Aarhus Univ., Aarhus 74-99
24. James R.C. Uniformly non-square Banach spaces. Ann. of Math. 80 (1964) 542-550
25. James R.C. Some self-dual properties of normed linear spaces. Symposium on Infinite-Dimensional Topology, 1967. Ann. of Math. Studies 69 (1972), Princeton Univ. Press 159-175
26. James R.C. Super-reflexive Banach spaces. Canad. J. Math. 24 (1972) 896-904
27. James R.C. A nonreflexive Banach space that is uniformly nonoctahedral. Israel J. Math. 18 (1974) 145-155
28. James R.C. Nonreflexive spaces of type 2. Israel J. Math. 30 (1978) 1-13
29. Janssen G. Restricted ultraproducts of finite von-Neumann algebras. Contributions to Non Standard Analysis (1972), North-Holland 101-114
30. Johnson W.B. On finite-dimensional subspaces of Banach spaces with local unconditional structure. Studia Math. 51 (1974) 223-238
31. Johnson W.B., and Lindenstrauss J. Basic concepts in the geometry of Banach spaces. In: Johnson W.B., and Lindenstrauss J. (Eds). Handbook of the Geometry of Banach Spaces Vol. 1 (2001), Elsevier, Amsterdam 1-84
32. p. Studia Math. 21 (1961) 161-176
33. Kahane J.P. Some random series of functions (1968), D. C. Heath and Co.
34. (in Russian). Kashin B. Sections of some finite-dimensional sets classes of smooth functions. Izv. Akad. Nauk SSSR 41 (1977) 344-351
35. Krivine J.L. Théorèmes de factorisation dans les espaces réticulés. Séminaire Maurey-Schwartz 1973-1974. Exp. Nos. 22 et 23 (1974), Ecole Polytech., Paris
36. Krivine J.L. Sous-espaces de dimension finie des espaces de Banach réticulés. Ann. of Math. 104 (1976) 1-29
37. Kwapień S. Isomorphic characterizations of inner product spaces by orthogonal series with vector valued coefficients. Studia Math. 44 (1972) 583-595
38. p dans un espace de Banach. Israel J. Math. 39 (1981) 341-348
39. p-spaces and their applications. Studia Math. 29 (1968) 275-326
40. Springer. Lindenstrauss J., and Tzafriri L. Classical Banach Spaces II: Function Spaces. Ergebnisse 97 (1979)
41. p. C.R. Acad. Sci. Paris 274 (1972) 1825-1828
42. p. Astérisque (1974), Société Mathématique de France, Paris No. 11
43. Maurey B. Un théorème de prolongement. C.R. Acad. Sci. Paris 279 (1974) 329-332
44. Maurey B., and Pisier G. Caractérisation d'une classe d'espaces de Banach par des propriétés de séries aléatoires vectorielles. C.R. Acad. Sci. Paris Sér. I 277 (1973) 687-690
45. Maurey B., and Pisier G. Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach. Studia Math. 58 (1976) 45-90
46. (translated from Russian). Milman V.D. A new proof of the theorem of A. Dvoretzky on sections of convex bodies. Functional Anal. Appl. 5 (1971) 28-37
47. Milman V.D. Almost Euclidean quotient spaces of subspaces of a finite-dimensional normed space. Proc. Amer. Math. Soc. 94 (1985) 445-449
48. Milman V.D., and Pisier G. Banach spaces with a weak cotype 2 property. Israel J. Math. 54 (1986) 139-158
49. Springer. Milman V.D., and Schechtman G. Asymptotic Theory of Finite-Dimensional Normed Spaces. Lecture Notes in Math. 1200 (1986)
50. (6). Nikishin E.M. Resonance theorems and superlinear operators. Uspekhi Mat. Nauk 25 156 (1970) 129-191
51. Nikishin E.M. A resonance theorem series in eigenfunctions of the Laplace operator. Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972) 795-813
52. 1967. Pietsch A. Absolut p-summierende Abbildungen in normierten Räumen. Studia Math. 28 (1966) 333-353
53. n. C.R. Acad. Sci. Paris Sér. 1277 (1973) 991-994
54. Pisier G. Martingales with values in uniformly convex spaces. Israel J. Math. 20 (1975) 326-350
55. Pisier G. Grothendieck's theorem for noncommutative C*-algebras with an appendix on Grothendieck's constants. J. Funct. Anal. 29 (1978) 397-415
56. Pisier G. Sur les espaces de Banach K-convexes. Seminar on Functional Analysis, 1979-1980. Exp. No. 11 (1980), Ecole Polytech., Palaiseau
57. Pisier G. Remarques sur un résultat non publié de B. Maurey. Seminar on Functional Analysis, 1980-1981. Exp. No. V (1981), Ecole Polytech., Palaiseau
58. Pisier G. Holomorphic semigroups the geometry of Banach spaces. Ann. of Math. 115 (1982) 375-392
59. p-sub space s of Banach spaces for 1p < 2. Trans. Amer. Math. Soc. 276 (1983) 201-211
60. Pisier G. Factorization of Linear Operators and Geometry of Banach Spaces. CBMS Regional Conference. Series in Math. 60 (1986), Amer. Math. Soc., Providence, RI
61. Pisier G. The Volume of Convex Bodies and Banach Space Geometry. Cambridge Tracts in Mathematics 94 (1989), Cambridge Univ. Press, Cambridge
62. p. Ann. of Math. 97 (1973) 344-373
63. Séminaire Laurent Schwartz 1969-1970: Applications radonifiantes (1970), Ecole Polytechnique, Paris
64. n. Bull. Acad. Polon. Sci. 26 (1978) 617-694
65. Szarek S., and Tomczak-Jaegermann N. On nearly Euclidean decomposition for some classes of Banach spaces. Compositio Math. 40 (1980) 367-385
66. p ( 1 ≤p < ∞). Studia Math. 50 (1974) 163-182