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Tytuł artykułu
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Warianty tytułu
Języki publikacji
Abstrakty
We show that the Schreier sets $S_α(α < ω_1)$ have the following dichotomy property. For every hereditary collection ℱ of finite subsets of ℱ, either there exists infinite $M = (m_i)_{i=1}^∞ ⊆ ℕ$ such that $S_α(M)={{m_i:i ∈ E}: E ∈ S_α} ⊆ ℱ$, or there exist infinite $M = (m_i)_{i=1}^∞, N ⊆ ℕ$ such that $ℱ[N](M) = {{m_i:i ∈ F}:F ∈ ℱ and F ⊂ N } ⊆ S_α$.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
245-256
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-09-08
Twórcy
autor
- Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078-0613, U.S.A., rjudd@math.okstate.edu
Bibliografia
- [AA] D. Alspach and S. Argyros, Complexity of weakly null sequences, Dissertationes Math. 321 (1992).
- [AO] D. Alspach and E. Odell, Averaging weakly null sequences, Lecture Notes in Math. 1332, Springer, 1988, 126-144.
- [AD] S. Argyros and I. Deliyanni, Examples of asymptotic $ℓ_1$ Banach spaces, preprint.
- [AMT] S. Argyros, S. Mercourakis and A. Tsarpalias, Convex unconditionality and summability of weakly null sequences, preprint.
- [FJ] T. Figiel and W. B. Johnson, A uniformly convex Banach space which contains no $ℓ_p$, Compositio Math. 29 (1974), 179-190.
- [KN] P. Kiriakouli and S. Negrepontis, Baire-1 functions and spreading models of $ℓ_1$, preprint.
- [OTW] E. Odell, N. Tomczak-Jaegermann and R. Wagner, Proximity to $ℓ_1$ and distortion in asymptotic $ℓ_1$ spaces, preprint.
- [Sch] J. Schreier, Gegenbeispiel zur Theorie der schwachen Konvergenz, Studia Math. 2 (1930), 58-62.
- [T] B. S. Tsirelson, Not every Banach space contains $ℓ_p$ or $c_0$, Functional Anal. Appl. 8 (1974), 138-141.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv132i3p245bwm