Sous-espaces des espaces de Banach

Bernard Maurey

Séminaire Bourbaki (1982-1983)

  • Volume: 25, page 199-215
  • ISSN: 0303-1179

How to cite

top

Maurey, Bernard. "Sous-espaces $l^P$ des espaces de Banach." Séminaire Bourbaki 25 (1982-1983): 199-215. <http://eudml.org/doc/110007>.

@article{Maurey1982-1983,
author = {Maurey, Bernard},
journal = {Séminaire Bourbaki},
keywords = {isomorphic subspaces},
language = {fre},
pages = {199-215},
publisher = {Société Mathématique de France},
title = {Sous-espaces $l^P$ des espaces de Banach},
url = {http://eudml.org/doc/110007},
volume = {25},
year = {1982-1983},
}

TY - JOUR
AU - Maurey, Bernard
TI - Sous-espaces $l^P$ des espaces de Banach
JO - Séminaire Bourbaki
PY - 1982-1983
PB - Société Mathématique de France
VL - 25
SP - 199
EP - 215
LA - fre
KW - isomorphic subspaces
UR - http://eudml.org/doc/110007
ER -

References

top
  1. [1] D.J. Aldous - Subspaces of L1 via random measures, Trans. Amer. Mat. Soc.267(1981), 445-463. Zbl0474.46007MR626483
  2. [2] N. Alon and V.D. Milman - Embedding of lk∞ in finite dimensional Banach spaces, à paraître. Zbl0546.46015
  3. [3] D. Amir and V.D. Milman - Unconditional and symmetric sets in n-dimensional normed spaces, Israel J. Math.37(1980), 3-20. Zbl0445.46011MR599298
  4. [4] K. Azuma - Weighted sums of certain dependent random variables, Tohoku Math. J.19(1967), 357-367. Zbl0178.21103MR221571
  5. [5] G. Bennett, V. Goodman, C.M. Newman - Norms of random matrices, Pacific J. Math.59(1975), 359-365. Zbl0325.47018MR393085
  6. [6] Y. Benyamini and Y. Gordon - Random factorization of operators between Banach spaces, Journal d'Analyse Mathématique39(1981), 45-74. Zbl0474.47010MR632456
  7. [7] J. Bourgain, D.H. Fremlin and M. Talagrand - Pointwise compact sets of Baire measurable functions, Amer. J. Math.100(1978), 845-886. Zbl0413.54016MR509077
  8. [8] J. Bourgain and H.P. Rosenthal - Applications of the theory of semi-embeddings to Banach space theory, à paraître. Zbl0541.46020
  9. [9] D.W. Boyd - Indices of function spaces and their relationship to interpolation, Canadian J. Math.21(1969), 1245-1254. Zbl0184.34802MR412788
  10. [10] J. Bretagnolle et D. Dacunha-Castelle - Application de l'étude de certaines formes linéaires aléatoires au plongement d'espaces de Banach dans des espaces Lp , Ann. Ecole Normale Sup.2(1969), 437-480. Zbl0229.60006MR265930
  11. [11] J. Bretagnolle, D. Dacunha-Castelle et J.-L. Krivine - Lois stables et espaces Lp , Ann. Inst. H. Poincaré2(1966), 231-259. Zbl0139.33501MR203757
  12. [12] A. Brunel and L. Sucheston - On B-convex Banach spaces, Math. System Th.7 (1974), 294-299. Zbl0323.46018MR438085
  13. [13] S. Chevet - Séries de variables aléatoires gaussiennes à valeurs dans E ⊗ε F, Séminaire sur la géométrie des espaces de Banach, exposé 19(1977-78), Ecole Polytechnique. Zbl0395.60004
  14. [14] D. Dacunha-Castelle et J.-L. Krivine - Sous-espaces de L1 , Israel J. Math.26(1977), 320-351. Zbl0344.46051MR626845
  15. [15] L. Dor - On sequences spanning a complex l1-space, Proc. Amer. Mat. Soc.47 (1975), 515-516. Zbl0296.46014MR358308
  16. [16] A. Dvoretzky - Some results on convex bodies and Banach spaces, Proc. Internat. Symp. on linear spaces, Jerusalem (1961), 123-160. Zbl0119.31803MR139079
  17. [17] A. Dvoretzky and C.A. Rogers - Absolute and unconditional convergence in normed linear spaces, Proc. Nat. Acad. Sci. USA36(1950), 192-197. Zbl0036.36303MR33975
  18. [18] G.A. Edgar and R.F. Wheeler - Topological properties of Banach spaces, à paraître. Zbl0506.46007
  19. [19] E. Ellentuck - A new proof that analytic sets are Ramsey, J. Symbolic Logic39(1974), 163-165. Zbl0292.02054MR349393
  20. [20] J. Elton - Sign embeddings of ln1 , à paraître. Zbl0525.46011
  21. [21] J. Farahat - Espaces de Banach contenant l1 , d'après H.P. Rosenthal, Séminaire Maurey-Schwartz, Ecole Polytechnique1973-74. Zbl0289.46014
  22. [22] T. Figiel - A short proof of Dvoretzky's theorem, Compositio Math.33(1976), 297-301. Zbl0343.52004MR487392
  23. [23] T. Figiel and W.B. Johnson - Large subspaces of ln∞and estimates of the Gordon-Lewis constant, Israel J. Math.37(1980), 92-112. Zbl0445.46012
  24. [24] T. Figiel, J. Lindenstrauss and V.D. Milman - The dimension of almost spherical sections of convex bodies, Acta Math.139(1977), 53-94. Zbl0375.52002MR445274
  25. [25] T. Figiel and N. Tomczak-Jaegermann - Projections onto Hilbertian subspaces of Banach spaces, Israel J. Math.33(1979), 155-171. Zbl0427.46010MR571251
  26. [26] E. Gluskin - The diameter of Minkowski compactum is approximately equal to n, Funct. Anal. Appl.15(1981), 57-58 (traduit du russe). Zbl0469.46017MR609798
  27. [27] G. Godefroy - Points de Namioka, espaces normants, applications à la théorie isométrique de la dualité, Israel J. Math.38(1981), 209-220. Zbl0453.46018MR605379
  28. [28] S. Guerre et M. Lévy - Espaces lp dans les sous-espaces de L1 , Trans. Amer. Mat. Soc. (1983). Zbl0527.46015MR709571
  29. [29] R. Haydon - Some more characterizations of Banach spaces containing l1 , Math. Proc. Camb. Phil. Soc.80(1976), 269-276. Zbl0335.46011MR423047
  30. [30] R.C. James - Uniformly non-square Banach spaces, Ann. of Math.80(1964), 542-550. Zbl0132.08902MR173932
  31. [31] R.C. James - Bases and reflexivity of Banach spaces, Ann. of Math.52(1950), 518-527. Zbl0039.12202MR39915
  32. [32] W.B. Johnson and J. Lindenstrauss - Extensions of Lipschitz mappings into a Hilbert space, à paraître. Zbl0539.46017
  33. [33] W.B. Johnson and H.P. Rosenthal - On w*-basic sequences and their applications to the study of Banach spaces, Studia Math.43(1972), 77-92. Zbl0213.39301MR310598
  34. [34] W.B. Johnson and G. Schechtman - Embedding lmp into ln1 , à paraître dans Acta Math.. 
  35. [35] M. Kadec and A. Pelczynski - Bases, lacunary sequences and conplemented subspaces in the spaces Lp , Studia Math.21(1962), 161-176. Zbl0102.32202MR152879
  36. [36] B. Kashin - Diameters of some finite dimensional sets and of some classes of smooth functions, Izv. A.N.S.S.R. Ser. Mat.41(1977), 334-351 (russe). MR481792
  37. [37] J.-L. Krivine - Sous-espaces de dimension finie des espaces de Banach réticulés, Ann. of Math.104(1976), 1-29. Zbl0329.46008MR407568
  38. [38] J.-L. Krivine et B. Maurey - Espaces de Banach stables, Israel J. Math.39 (1981), 273-295. Zbl0504.46013MR636897
  39. [39] H. Lemberg - Nouvelle démonstration d'un théorème de J.-L. Krivine sur la finie représentation de lp dans un espace de Banach, Israel J. Math.39 (1981), 341-348. Zbl0466.46023MR636901
  40. [40] P. Lévy - Problèmes concrets d'analyse fonctionnelle, Gauthier-Villars1951. Zbl0043.32302MR41346
  41. [41] J. Lindenstrauss and L. Tzafriri - On the complemented subspaces problem, Israel J. Math.9(1971), 263-269. Zbl0211.16301MR276734
  42. [42] J. Lindenstrauss and L. Tzafriri - On Orlicz sequence spaces, Israel J. Math.10(1971), 379-390. Zbl0227.46042MR313780
  43. [43] J. Lindenstrauss and L. Tzafriri - Classical Banach spaces I, Sequence spaces, Ergebnisse 92, Springer1977. Zbl0362.46013MR500056
  44. [44] J. Lindenstrauss and L. Tzafriri - Classical Banach spaces II, Function Spaces, Ergebnisse 97, Springer1979. Zbl0403.46022MR540367
  45. [45] M.B. Marcus and G. Pisier - Characterizations of almost surely continuous p-stable random Fourier series and strongly stationary processes, à paraître. Zbl0547.60047
  46. [46] B. Maurey - Construction de suites symétriques, C.R.A.S. Paris288(1979), 679-681. Zbl0398.46019MR533901
  47. [47] B. Maurey et G. Pisier - Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach, Studia Math.58 (1976), 45-90. Zbl0344.47014MR443015
  48. [48] V.D. Milman - New proof of the theorem of Dvoretzky on sections of convex bodies, Funct. Anal. Appl.5(1971), 28-37 (traduit du russe). Zbl0239.46018MR293374
  49. [49] V.D. Milman - Some remarks about embeddings of lk1 in finite dimensional spaces, Israel J. Math.43(1982), 129-138. Zbl0512.46016MR689972
  50. [50] E. Odell and H.P. Rosenthal - A double-dual characterization of separable Banach spaces containing l1 , Israel J. Math.20(1975), 375-384. Zbl0312.46031MR377482
  51. [51] A. Pajor - Plongement de l1n dans les espaces de Banach complexes, à paraître. Zbl0546.46016
  52. [52] A. Pelczynski - Geometry of finite dimensional Banach spaces and operator ideals, Notes in Banach spaces, University of Texas Press. Zbl0461.46014MR606222
  53. [53] G. Pisier - Sur les espaces de Banach qui ne contiennent pas uniformément de l1n , C.R.A.S. Paris277(1973), 991-993. Zbl0271.46011MR333673
  54. [54] G. Pisier - Holomorphic semi-groups and the geometry of Banach spaces, Ann. of Math.115(1982), 375-392. Zbl0487.46008MR647811
  55. [55] G. Pisier - De nouvelles caractérisations des ensembles de Sidon, Advances in Math. (supplementary studies) vol. 7B(1981), 685. Zbl0468.43008MR634264
  56. [56] G. Pisier - On the dimension of the lnp-subspaces of Banach spaces, for 1 ≤ p &lt; 2 , Trans. Amer. Mat. Soc. (1983). Zbl0509.46016
  57. [57] H.P. Rosenthal - On subspaces of Lp , Ann. of Math.97(1973), 344-373. Zbl0253.46049MR312222
  58. [58] H.P. Rosenthal - A characterization of Banach spaces containing l1, Proc. Nat. Acad. Sci. USA71(1974), 2411-2413. Zbl0297.46013MR358307
  59. [59] H.P. Rosenthal - Pointwise compact subsets of the first Baire class, Amer. J. Math.99(1977), 362-378. Zbl0392.54009MR438113
  60. [60] H.P. Rosenthal - Sign-embeddings of L1 , à paraître. 
  61. [61] N. Sauer - On the density of families of sets, Journal of combinatorial Theory13(1972), 145-147. Zbl0248.05005MR307902
  62. [62] G. Schechtman - Random embeddings of euclidean spaces in sequence spaces, Israel J. Math.40(1981), 187-192. Zbl0474.46004MR634905
  63. [63] E. Schmidt - Die Brunn-Minkowski Ungleichung, Math. Nachr.1(1948), 81-157. Zbl0030.07602MR28600
  64. [64] D. Slepian - The one-sided barrier problem for gaussian noise, Bell System Tech. J.41(1962), 463-501. MR133183
  65. [65] A. Szankowski - On Dvoretzky's theorem on almost spherical sections of convex bodies, Israel J. Math.17(1974), 325-338. Zbl0288.52002MR350388
  66. [66] S. Szarek - On the best constants in the Khintchine inequality, Studia Math.58(1976), 197-208. Zbl0424.42014MR430667
  67. [67] S. Szarek and N. Tomczak-Jaegermann - On nearly euclidean decomposition for some classes of Banach spaces, Compositio Math.40(1980), 367-385. Zbl0432.46018MR571056
  68. [68] S. Szarek - The finite dimensional basis problem with an appendix on nets of Grassman manifold, à paraître. Zbl0554.46004
  69. [69] B.S. Tsirelson - Not every Banach space contains lp or co , Funct. Anal. Appl.8(1974), 138-141 (traduit du russe). Zbl0296.46018
  70. [70] L. Tzafriri - On Banach spaces with unconditional bases, Israel J. Math.17 (1974), 84-93. Zbl0281.46013MR348456

NotesEmbed ?

top

You must be logged in to post comments.