Stability of positive part of unit ball in Orlicz spaces

Ryszard Grzaślewicz; Witold Seredyński

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 3, page 413-424
  • ISSN: 0010-2628

Abstract

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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 Φ : Q × Q → Q , Φ ( 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 ϕ ( μ ) the stability of the positive part of the unit ball is equivalent to the stability of the unit ball.

How to cite

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Grzaślewicz, Ryszard, and Seredyński, Witold. "Stability of positive part of unit ball in Orlicz spaces." Commentationes Mathematicae Universitatis Carolinae 46.3 (2005): 413-424. <http://eudml.org/doc/249548>.

@article{Grzaślewicz2005,
abstract = {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.},
author = {Grzaślewicz, Ryszard, Seredyński, Witold},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {stable convex set},
language = {eng},
number = {3},
pages = {413-424},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Stability of positive part of unit ball in Orlicz spaces},
url = {http://eudml.org/doc/249548},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Grzaślewicz, Ryszard
AU - Seredyński, Witold
TI - Stability of positive part of unit ball in Orlicz spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 3
SP - 413
EP - 424
AB - 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.
LA - eng
KW - stable convex set
UR - http://eudml.org/doc/249548
ER -

References

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