Some remarks on ultrapowers and superproperties of the sum and interpolation spaces of Banach spaces

Yves Raynaud

Compositio Mathematica (1991)

  • Volume: 79, Issue: 3, page 295-319
  • ISSN: 0010-437X

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Raynaud, Yves. "Some remarks on ultrapowers and superproperties of the sum and interpolation spaces of Banach spaces." Compositio Mathematica 79.3 (1991): 295-319. <http://eudml.org/doc/90109>.

@article{Raynaud1991,
author = {Raynaud, Yves},
journal = {Compositio Mathematica},
keywords = {structure of ultrapowers; sums of rearrangement invariant function spaces; equiintegrability conditions; superstability; real Lions-Peetre interpolation; Lorentz spaces},
language = {eng},
number = {3},
pages = {295-319},
publisher = {Kluwer Academic Publishers},
title = {Some remarks on ultrapowers and superproperties of the sum and interpolation spaces of Banach spaces},
url = {http://eudml.org/doc/90109},
volume = {79},
year = {1991},
}

TY - JOUR
AU - Raynaud, Yves
TI - Some remarks on ultrapowers and superproperties of the sum and interpolation spaces of Banach spaces
JO - Compositio Mathematica
PY - 1991
PB - Kluwer Academic Publishers
VL - 79
IS - 3
SP - 295
EP - 319
LA - eng
KW - structure of ultrapowers; sums of rearrangement invariant function spaces; equiintegrability conditions; superstability; real Lions-Peetre interpolation; Lorentz spaces
UR - http://eudml.org/doc/90109
ER -

References

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  1. [1] Arazy J.: The K-functional of certain pairs of rearrangement invariant spaces. Bull. Austral. Math. Soc.27 (1983) 249-257. Zbl0512.46056MR707975
  2. [2] Bastero, J., Raynaud, Y.: Quotients and interpolation spaces of stable Banach spaces. Studia Math.93 (1989) p. 223-239. Zbl0714.46053MR1030489
  3. [3] Bergh, J., Löfström, J.: Interpolation Spaces, an Introduction. Springer Verlag (1976). Zbl0344.46071MR482275
  4. [4] Dacunha-Castelle, D.: Sur un théorème de J. L. Krivine concernant la caractérisation des classes d'espaces isomorphes à des espaces d'Orlicz généralisés. Isr. J. Math., 13, 1972, p. 261-276. Zbl0262.46033MR326370
  5. [5] Dacunha-Castelle, D., Krivine, J.L.: Application des ultraproduits à l'étude des espaces et algèbres de Banach. Studia Math.41, (1972), p. 315-334. Zbl0275.46023MR305035
  6. [6] Heinrich, S.: Ultraproducts in Banach Space Theory. J. Reine Angew. Math.313, (1980) p. 72-104. Zbl0412.46017MR552464
  7. [7] Holmstedt, T.: Interpolation of quasi-normed spaces. Math. Scand.26, 177-199 (1970). Zbl0193.08801MR415352
  8. [8] Krivine, J.L., Maurey, B.: Espaces de Banach stables. Israel J. of Math. 39, no. 4, (1981) p. 273-295. Zbl0504.46013MR636897
  9. [9] Lorentz, G.G.: Some new functional spaces. Ann. Math.51, (1950), p. 37-55. Zbl0035.35602MR33449
  10. [10] Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces, II, Functions spaces. Springer-Verlag (1979). Zbl0403.46022MR540367
  11. [11] Maligranda, L.: The K-functional for symmetric spaces, in: Interpolation space and Allied Topics in Analysis. Lecture notes in Mathematics no. 1070, Springer Verlag (1984). Zbl0573.46045MR760482
  12. [12] Raynaud, Y.: Espaces de Banach superstables, distances stables et homéomorphismes uniformes. Isr. J. Math.44, no. 1, (1983) p. 33-52. Zbl0537.46023MR693653
  13. [13] Raynaud, Y.: Sur la propriété de stabilité pour les espaces de Banach. Thèse 3° Cycle (1981), Université Paris VII. 
  14. [14] Raynaud, Y.: Abstract E(Lϕ) spaces. Preprint. 
  15. [15] Schütt, C.: Lorentz spaces that are isomorphic to subspaces of L1. Trans. Amer. Math. Soc.314, (1989), p. 583-595. Zbl0651.46028MR974527
  16. [16] Weiss, L.: Banach lattices with the subsequence Splitting Property. Proc. Amer. Math. Soc. 105, no. 1, (1989), 87-96. Zbl0679.46018MR937853
  17. [17] Lorentz, G.G., Shimogaki, T., Interpolation Theorems for Operators in Function Spaces, Journal of Functional Analysis2, (1968), p. 31-51. Zbl0162.44504MR257775

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