- Tytuł:
- Asymptotically isometric and isometric copies of \(\ell_1\) in some Banach function lattices
- Autorzy:
-
Kamińska, Anna
~Mastyło, Mieczysław - Powiązania:
- https://bibliotekanauki.pl/articles/1912874.pdf
- Data publikacji:
- 2013
- Wydawca:
- Polskie Towarzystwo Matematyczne
- Tematy:
-
Caldern-Lozanovskii spaces
Orlicz-Lorentz spaces
Orlicz spaces
Lorentz spaces
Marcinkiewicz spaces
isometric copies of \(\ell_1^{(n)}\) and \(\ell_1\)
asymptotically isometric copies of \(\ell_1\)
fixed point property - Opis:
- We identify the class of Caldern-Lozanovskii spaces that do not contain an asymptotically isometric copy of \(\ell_1\), and consequently we obtain the corresponding characterizations in the classes of Orlicz-Lorentz and Orlicz spaces equipped with the Luxemburg norm. We also give a~complete description of order continuous Orlicz-Lorentz spaces which contain (order) isometric copies of \(\ell_1^{(n)}\) for each integer \(n \geq 2\).~As an application we provide necessary and sufficient conditions for order continuous Orlicz-Lorentz spaces to contain an (order) isometric copy of \(\ell_1\).~In particular we give criteria in Orlicz and Lorentz spaces for (order) isometric containment of \(\ell_1^{(n)}\) and \(\ell_1\).~The results are applied to obtain the~description of universal Orlicz-Lorentz spaces for all two-dimensional normed spaces.
- Źródło:
-
Commentationes Mathematicae; 2013, 53, 2; 383-400
0373-8299 - Pojawia się w:
- Commentationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł