Locally nonconical unit balls in Orlicz spaces

• Autorzy: Ryszard Grząślewicz , Witold Seredyński
• Języki publikacji: EN

Abstrakty

EN

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 \(E^\varphi (\mu)\).

Słowa kluczowe

EN

stable convex set

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2007
• Tom: 47
• Numer: 1

Daty

wydano

2007

online

2017-12-19

Twórcy

autor

Ryszard Grząślewicz

autor

Witold Seredyński

Identyfikatory

DOI

10.14708/cm.v47i1.5240