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## Studia Mathematica

2000 | 141 | 3 | 273-300
Tytuł artykułu

### On the complemented subspaces of the Schreier spaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is shown that for every 1 ≤ ξ < ω, two subspaces of the Schreier space $X^ξ$ generated by subsequences $(e_{l_n}^{ξ})$ and $(e_{m_n}^{ξ})$, respectively, of the natural Schauder basis $(e_{n}^{ξ})$ of $X^ξ$ are isomorphic if and only if $(e_{l_n}^{ξ})$ and $(e_{m_n}^{ξ})$ are equivalent. Further, $X^ξ$ admits a continuum of mutually incomparable complemented subspaces spanned by subsequences of $(e_{n}^{ξ})$. It is also shown that there exists a complemented subspace spanned by a block basis of $(e_{n}^{ξ})$, which is not isomorphic to a subspace generated by a subsequence of $(e_n^ζ)$, for every $0 ≤ ζ ≤ ξ$. Finally, an example is given of an uncomplemented subspace of $X^ξ$ which is spanned by a block basis of $(e_{n}^{ξ})$.
Słowa kluczowe
EN
Czasopismo
Rocznik
Tom
Numer
Strony
273-300
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-12-01
poprawiono
2000-02-14
Twórcy
autor
• Department of Mathematics, Oklahoma State University, Stillwater, OK 74078-1058, U.S.A.
autor
• Department of Mathematics, National University of Singapore, Singapore 117543
Bibliografia
• [1] D. E. Alspach and S. A. Argyros, Complexity of weakly null sequences, Dissertationes Math. 321 (1992).
• [2] G. Androulakis and E. Odell, Distorting mixed Tsirelson spaces, Israel J. Math. 109 (1999), 125-149.
• [3] S. A. Argyros and I. Deliyanni, Examples of asymptotic $l_1$ Banach spaces, Trans. Amer. Math. Soc. 349 (1997), 973-995.
• [4] S. A. Argyros and V. Felouzis, Interpolating hereditarily indecomposable Banach spaces, J. Amer. Math. Soc. 13 (2000), 243-294.
• [5] S. A. Argyros and I. Gasparis, Unconditional structures of weakly null sequences, Trans. Amer. Math. Soc., to appear.
• [6] S. A. Argyros, S. Mercourakis and A. Tsarpalias, Convex unconditionality and summability of weakly null sequences, Israel J. Math. 107 (1998), 157-193.
• [7] P. Cembranos, The hereditary Dunford-Pettis property on C(K,E), Illinois J. Math. 31 (1987), 365-373.
• [8] I. Gasparis, A dichotomy theorem for subsets of the power set of the natural numbers, Proc. Amer. Math. Soc., to appear.
• [9] A. Kechris, Classical Descriptive Set Theory, Grad. Texts in Math. 156, Springer, New York, 1994.
• [10] K. Kuratowski, Applications of the Baire-category method to the problem of independent sets, Fund. Math. 81 (1973), 65-72.
• [11] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, II, Ergeb. Math. Grenzgeb. 92, 97, Springer, Berlin, 1977, 1979.
• [12] J. Mycielski, Almost every function is independent, Fund. Math. 81 (1973), 43-48.
• [13] E. Odell, On quotients of Banach spaces having shrinking unconditional bases, Illinois J. Math. 36 (1992), 681-695.
• [14] E. Odell, N. Tomczak-Jaegermann and R. Wagner, Proximity to $l_1$ and distortion in asymptotic $l_1$ spaces, J. Funct. Anal. 150 (1997), 101-145.
• [15] J. Schreier, Ein Gegenbeispiel zur Theorie der schwachen Konvergenz, Studia Math. 2 (1930), 58-62.
Typ dokumentu
Bibliografia
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