A Banach space block finitely universal for monotone bases
HTML articles powered by AMS MathViewer
- by E. Odell and Th. Schlumprecht PDF
- Trans. Amer. Math. Soc. 352 (2000), 1859-1888 Request permission
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 $X$.References
- S. A. Argyros and I. Deliyanni, Examples of asymptotic $l_1$ Banach spaces, Trans. Amer. Math. Soc. 349 (1997), no. 3, 973–995. MR 1390965, DOI 10.1090/S0002-9947-97-01774-1
- Steven F. Bellenot, Richard Haydon, and Edward Odell, Quasi-reflexive and tree spaces constructed in the spirit of R. C. James, Banach space theory (Iowa City, IA, 1987) Contemp. Math., vol. 85, Amer. Math. Soc., Providence, RI, 1989, pp. 19–43. MR 983379, DOI 10.1090/conm/085/983379
- Peter G. Casazza and Thaddeus J. Shura, Tsirel′son’s space, Lecture Notes in Mathematics, vol. 1363, Springer-Verlag, Berlin, 1989. With an appendix by J. Baker, O. Slotterbeck and R. Aron. MR 981801, DOI 10.1007/BFb0085267
- T. Figiel and W. B. Johnson, A uniformly convex Banach space which contains no $l_{p}$, Compositio Math. 29 (1974), 179–190. MR 355537
- W. T. Gowers and B. Maurey, The unconditional basic sequence problem, J. Amer. Math. Soc. 6 (1993), no. 4, 851–874. MR 1201238, DOI 10.1090/S0894-0347-1993-1201238-0
- Robert C. James, Uniformly non-square Banach spaces, Ann. of Math. (2) 80 (1964), 542–550. MR 173932, DOI 10.2307/1970663
- J. L. Krivine, Sous-espaces de dimension finie des espaces de Banach réticulés, Ann. of Math. (2) 104 (1976), no. 1, 1–29. MR 407568, DOI 10.2307/1971054
- H. Lemberg, Nouvelle démonstration d’un théorème de J.-L. Krivine sur la finie représentation de $l_{p}$ dans un espace de Banach, Israel J. Math. 39 (1981), no. 4, 341–348 (French, with English summary). MR 636901, DOI 10.1007/BF02761678
- B. Maurey, V. D. Milman, and N. Tomczak-Jaegermann, Asymptotic infinite-dimensional theory of Banach spaces, Geometric aspects of functional analysis (Israel, 1992–1994) Oper. Theory Adv. Appl., vol. 77, Birkhäuser, Basel, 1995, pp. 149–175. MR 1353458
- B. Maurey and H. P. Rosenthal, Normalized weakly null sequence with no unconditional subsequence, Studia Math. 61 (1977), no. 1, 77–98. MR 438091, DOI 10.4064/sm-61-1-77-98
- E. Odell and Th. Schlumprecht, On the richness of the set of $p$’s in Krivine’s theorem, Geometric aspects of functional analysis (Israel, 1992–1994) Oper. Theory Adv. Appl., vol. 77, Birkhäuser, Basel, 1995, pp. 177–198. MR 1353459
- Vlastimil Pták, A combinatorial theorem on systems of inequalities and its application to analysis, Czechoslovak Math. J. 9(84) (1959), 629–630 (English, with Russian summary). MR 110007
- B. S. Tsirelson, Not every Banach space contains $\ell _{p}$ or $c_{0}$, Funct. Anal. Appl. 8 (1974), 138–141.
Additional Information
- E. Odell
- Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712-1082
- Email: odell@math.utexas.edu
- Th. Schlumprecht
- Affiliation: Department of Mathematics, Texas A & M University, College Station, Texas 77843
- MR Author ID: 260001
- Email: thomas.schlumprecht@math.tamu.edu
- Received by editor(s): May 24, 1996
- Published electronically: October 29, 1999
- Additional Notes: Research supported by NSF and TARP
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 352 (2000), 1859-1888
- MSC (1991): Primary 46B20; Secondary 46B15, 46B03
- DOI: https://doi.org/10.1090/S0002-9947-99-02425-3
- MathSciNet review: 1637094