Locally nonconical unit balls in Orlicz spaces

• Autorzy: Grząślewicz R. , Seredyński W.
• 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 6 Q there exists an open neighbourhood U of x such that (U Q) + (y - x)/2 C Q- The following theorem is established: An Orlicz space Lv{pi) has an LNC unit ball if and only if either L[fi](u) is finite dimensional or the measure fi is atomic with a positive greatest lower bound and tp satisfies the condition Aj!(/i) and is strictly convex on the interval [0,b], or c[fi] = +oo and [fi] satisfies the condition and is strictly convex on K. A similar result is obtained for the space E[fi](u).

Słowa kluczowe

EN

stable convex set

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2007
• Tom: Vol. 47, [Z] 1
• Strony: 85--107
• Opis fizyczny: bibliogr. 23 poz.

Twórcy

autor

Grząślewicz R.

autor

Seredyński W.

• Institute of Mathematics, Wrocław University of Technology Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland,

Bibliografia

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