- Tytuł:
- Rotundity and smoothness of convex bodies in reflexive and nonreflexive spaces
- Autorzy:
-
Klee, Victor
Veselý, Libor
Zanco, Clemente - Powiązania:
- https://bibliotekanauki.pl/articles/1287312.pdf
- Data publikacji:
- 1996
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
normed linear space
reflexive
convex body
smooth
rotund
strictly convex
vector sum
convex hull
stability - Opis:
- For combining two convex bodies C and D to produce a third body, two of the most important ways are the operation ∓ of forming the closure of the vector sum C+D and the operation γ̅ of forming the closure of the convex hull of C ⋃ D. When the containing normed linear space X is reflexive, it follows from weak compactness that the vector sum and the convex hull are already closed, and from this it follows that the class of all rotund bodies in X is stable with respect to the operation ∓ and the class of all smooth bodies in X is stable with respect to both ∓ and γ̅. In our paper it is shown that when X is separable, these stability properties of rotundity (resp. smoothness) are actually equivalent to the reflexivity of X. The characterizations remain valid for each nonseparable X that contains a rotund (resp. smooth) body.
- Źródło:
-
Studia Mathematica; 1996, 120, 3; 191-204
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł