Geodesic
Stability of positive part of unit ball in Orlicz spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 3, pp. 413-424 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The aim of this paper is to investigate the stability of the positive part of the unit ball in Orlicz spaces, endowed with the Luxemburg norm. The convex set $Q$ in a topological vector space is stable if the midpoint map $\Phi\colon Q\times Q\rightarrow Q$, $\Phi(x,y) =(x+y)/2$ is open with respect to the inherited topology in $Q$. The main theorem is established: In the Orlicz space $L^\varphi(\mu)$ the stability of the positive part of the unit ball is equivalent to the stability of the unit ball.
The aim of this paper is to investigate the stability of the positive part of the unit ball in Orlicz spaces, endowed with the Luxemburg norm. The convex set $Q$ in a topological vector space is stable if the midpoint map $\Phi\colon Q\times Q\rightarrow Q$, $\Phi(x,y) =(x+y)/2$ is open with respect to the inherited topology in $Q$. The main theorem is established: In the Orlicz space $L^\varphi(\mu)$ the stability of the positive part of the unit ball is equivalent to the stability of the unit ball.
Classification : 46Axx, 46B20, 46Cxx, 46E30, 52A41
Keywords: stable convex set 
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     title = {Stability of positive part of unit ball in {Orlicz} spaces},
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Grząślewicz, Ryszard; Seredyński, Witold. Stability of positive part of unit ball in Orlicz spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 3, pp. 413-424. http://geodesic.mathdoc.fr/item/CMUC_2005_46_3_a4/