- Tytuł:
- On the complemented subspaces of the Schreier spaces
- Autorzy:
-
Gasparis, I.
Leung, D. - Powiązania:
- https://bibliotekanauki.pl/articles/1206028.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Schreier sets
complemented subspace - Opis:
- 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 $(e_{n}^{ξ})$.
- Źródło:
-
Studia Mathematica; 2000, 141, 3; 273-300
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł