- Tytuł:
- From weak to strong types of $L_{E}^{1}$-convergence by the Bocce criterion
- Autorzy:
-
J. Balder, Erik
Girardi, Maria
Jalby, Vincent - Powiązania:
- https://bibliotekanauki.pl/articles/1290125.pdf
- Data publikacji:
- 1994
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- Necessary and sufficient oscillation conditions are given for a weakly convergent sequence (resp. relatively weakly compact set) in the Bochner-Lebesgue space $ℒ_{E}^{1}$ to be norm convergent (resp. relatively norm compact), thus extending the known results for $ℒ_{ℝ}^{1}$. Similarly, necessary and sufficient oscillation conditions are given to pass from weak to limited (and also to Pettis-norm) convergence in $ℒ_{E}^{1}$. It is shown that tightness is a necessary and sufficient condition to pass from limited to strong convergence. Other implications between several modes of convergence in $ℒ_{E}^{1}$ are also studied.
- Źródło:
-
Studia Mathematica; 1994, 111, 3; 241-262
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł