- Tytuł:
- A new convexity property that implies a fixed point property for $L_{1}$
- Autorzy:
- Lennard, Chris
- Powiązania:
- https://bibliotekanauki.pl/articles/1293465.pdf
- Data publikacji:
- 1991
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
uniform Kadec-Klee property
convergence in measure compact sets
convex sets
normal structure
Lebesgue function spaces
fixed point
nonexpansive mapping
Chebyshev centre - Opis:
- In this paper we prove a new convexity property for L₁ that resembles uniform convexity. We then develop a general theory that leads from the convexity property through normal structure to a fixed point property, via a theorem of Kirk. Applying this theory to L₁, we get the following type of normal structure: any convex subset of L₁ of positive diameter that is compact for the topology of convergence locally in measure, must have a radius that is smaller than its diameter. Indeed, a stronger result holds. The Chebyshev centre of any norm bounded, convergence locally in measure compact subset of L₁ must be norm compact. Immediately from normal structure, we get a new proof of a fixed point theorem for L₁ due to Lami Dozo and Turpin.
- Źródło:
-
Studia Mathematica; 1991, 100, 2; 95-108
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł