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1999 | 133 | 3 | 275-294
Tytuł artykułu

Uniqueness of unconditional bases in $c_0$-products

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EN
Abstrakty
EN
We give counterexamples to a conjecture of Bourgain, Casazza, Lindenstrauss and Tzafriri that if X has a unique unconditional basis (up to permutation) then so does $c_0(X)$. We also give some positive results including a simpler proof that $c_0(ℓ_1)$ has a unique unconditional basis and a proof that $c_0(ℓ_{p_n}^{N_n})$ has a unique unconditional basis when $p_n ↓ 1$, $N_{n+1} ≥ 2N_{n}$ and $(p_n-p_{n+1}) logN_{n}$ remains bounded.
Słowa kluczowe
Czasopismo
Rocznik
Tom
133
Numer
3
Strony
275-294
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-05-15
Twórcy
autor
Bibliografia
  • [1] B. Bollobas, Combinatorics, Cambridge Univ. Press, 1986.
  • [2] J. Bourgain, On the Dunford-Pettis property, Proc. Amer. Math. Soc. 81 (1981), 265-272.
  • [3] J. Bourgain, P. G. Casazza, J. Lindenstrauss and L. Tzafriri, Banach spaces with a unique unconditional basis, up to a permutation, Mem. Amer. Math. Soc. 322 (1985).
  • [4] P. G. Casazza and N. J. Kalton, Uniqueness of unconditional bases in Banach spaces, Israel J. Math. 103 (1998), 141-176.
  • [5] P. G. Casazza and T. J. Schura, Tsirelson's Space, Lecture Notes in Math. 1363, Springer, 1989.
  • [6] I. S. Edelstein and P. Wojtaszczyk, On projections and unconditional bases in direct sums of Banach spaces, Studia Math. 56 (1976), 263-276.
  • [7] T. Figiel, J. Lindenstrauss and V. D. Milman, The dimension of almost spherical sections of convex bodies, Acta Math. 139 (1977), 53-94.
  • [8] W. T. Gowers, A solution to Banach's hyperplane problem, Bull. London Math. Soc. 26 (1994), 523-530.
  • [9] G. Köthe and O. Toeplitz, Lineare Räume mit unendlich vielen Koordinaten und Ringen unendlicher Matrizen, J. Reine Angew. Math. 171 (1934), 193-226.
  • [10] J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in $L_p$-spaces and their applications, Studia Math. 29 (1968), 315-349.
  • [11] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I. Sequence Spaces, Springer, 1977.
  • [12] J. Lindenstrauss and M. Zippin, Banach spaces with a unique unconditional basis, J. Funct. Anal. 3 (1969), 115-125.
  • [13] V. D. Milman and G. Schechtman, Asymptotic Theory of Finite-Dimensional Spaces, Lecture Notes in Math. 1200, Springer, 1986.
  • [14] B. S. Mityagin, Equivalence of bases in Hilbert scales, Studia Math. 37 (1970), 111-137 (in Russian).
  • [15] G. Pisier, The Volume of Convex Bodies and Geometry of Banach Spaces, Cambridge Tracts in Math. 94, Cambridge Univ. Press, 1989.
  • [16] P. Wojtaszczyk, Uniqueness of unconditional bases in quasi-Banach spaces with applications to Hardy spaces, II, Israel J. Math 97 (1997), 253-280.
  • [17] M. Wojtowicz, On Cantor-Bernstein type theorems in Riesz spaces, Indag. Math. 91 (1988), 93-100.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv133i3p275bwm
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