- Tytuł:
- Locally nonconical unit balls in Orlicz spaces
- Autorzy:
-
Grząślewicz, Ryszard
Seredyński, Witold - Powiązania:
- https://bibliotekanauki.pl/articles/745940.pdf
- Data publikacji:
- 2007
- Wydawca:
- Polskie Towarzystwo Matematyczne
- Tematy:
- stable convex set
- Opis:
- The aim of this paper is to investigate the local nonconicality of unit ball in Orlicz spaces, endowed with the Luxemburg norm. A closed convex set \(Q\) in a locally convex topological Hausdorff space \(X\) is called locally nonconical \((LNC)\), if for every \(x, y \in Q\) there exists an open neighbourhood \(U\) of \(x\) such that \((U\cap Q) + (y - x)/2 \subset Q\). The following theorem is established: An Orlicz space \(L^\varphi(\mu)\) has an \(LNC\) unit ball if and only if either \(L^\varphi (\mu)\) is finite dimensional or the measure \(\mu\) is atomic with a positive greatest lower bound and \(\varphi\) satisfies the condition \(\delta_r^0(\mu)\) and is strictly convex on the interval \([0, b]\), or \(c(\varphi) = +\infty\) and \(\varphi\) satisfies the condition \(\Delta_2 (\mu)\) and is strictly convex on \(\mathbb{R}\). A similar result is obtained for the space \(E^\varphi (\mu)\).
- Źródło:
-
Commentationes Mathematicae; 2007, 47, 1
0373-8299 - Pojawia się w:
- Commentationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł