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Transactions of the American Mathematical Society

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A Banach space block finitely universal for monotone bases

Authors: E. Odell and Th. Schlumprecht
Journal: Trans. Amer. Math. Soc. 352 (2000), 1859-1888
MSC (1991): Primary 46B20; Secondary 46B15, 46B03
Published electronically: October 29, 1999
MathSciNet review: 1637094
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Abstract: A reflexive Banach space $X$ with a basis $(e_{i})$ is constructed having the property that every monotone basis is block finitely representable in each block basis of $X$.

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  • [AD] S. Argyros and I. Deliyanni, Examples of asymptotically $\ell ^{1}$ Banach spaces, Trans. Amer. Math. Soc. 349 (1997), 973-955. MR 97f:46021
  • [BHO] S. Bellenot, R. Haydon and E. Odell, Quasi-reflexive and tree spaces constructed in the spirit of R.C. James, Contemporary Math. 85 (1989), 19-43. MR 89m:46014
  • [CS] P.G. Casazza and T.J. Shura, Tsirel$'$son's Space, Lectures Notes in Math., vol. 1363, Springer-Verlag, Berlin and New York, 1989. MR 90b:46030
  • [FJ] T. Figiel and W.B. Johnson, A uniformly convex Banach space which contains no $\ell _{p}$, Compositio Math. 29 (1974), 179-190. MR 50:8011
  • [GM] W.T. Gowers and B. Maurey, The unconditional basic sequence problem, J. Amer. Math. Soc. 6 (1993), 851-874. MR 94k:46021
  • [J] R.C. James, Uniformly nonsquare Banach spaces, Ann. Math. 80 (1964), 542-550. MR 30:4139
  • [K] J.L. Krivine, Sous-espaces de dimension finie des espaces de Banach réticulés, Ann. of Math. 104 (1976), 1-29. MR 53:11341
  • [L] H. Lemberg, Nouvelle démonstration d'un theorem de J.L. Krivine sur la finie representation de $\ell _{p}$ dans un espace de Banach, Israel Journal of Mathematics 39 (1981), 391-398. MR 83b:46015
  • [MMT] B. Maurey, V.D. Milman and N. Tomczak-Jaegermann, Asymptotic infinite-dimensional theory of Banach spaces, Operator Theory, Advances and Applications 77 (1995), 149-175. MR 97g:46015
  • [MR] B. Maurey and H. Rosenthal, Normalized weakly null sequences with no unconditional subsequences, Studia Math. 61 (1971), 77-98. MR 55:11010
  • [OS] E. Odell and Th. Schlumprecht, On the richness of the set of $p$'s in Krivine's theorem, Operator Theory, Advances and Applications 77 (1995), 177-198. MR 96i:46015
  • [P] V. Ptak, A combinatorial theorem on systems of inequalities and its application to analysis, Czech. Math. J. 84 (1959), 629-630. MR 22:890
  • [T] B. S. Tsirelson, Not every Banach space contains $\ell _{p}$ or $c_{0}$, Funct. Anal. Appl. 8 (1974), 138-141.

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Additional Information

E. Odell
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712-1082

Th. Schlumprecht
Affiliation: Department of Mathematics, Texas A & M University, College Station, Texas 77843

Keywords: Unconditional basic sequence, block finitely universal
Received by editor(s): May 24, 1996
Published electronically: October 29, 1999
Additional Notes: Research supported by NSF and TARP
Article copyright: © Copyright 2000 American Mathematical Society

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