- Tytuł:
- Analytic and $C^k$ approximations of norms in separable Banach spaces
- Autorzy:
-
Deville, Robert
Fonf, Vladimir
Hájek, Petr - Powiązania:
- https://bibliotekanauki.pl/articles/1287379.pdf
- Data publikacji:
- 1996
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
analytic norm
approximation
convex function
geometry of Banach spaces - Opis:
- We prove that in separable Hilbert spaces, in $ℓ_{p}(ℕ)$ for p an even integer, and in $L_{p}[0,1]$ for p an even integer, every equivalent norm can be approximated uniformly on bounded sets by analytic norms. In $ℓ_{p}(ℕ)$ and in $L_{p}[0,1]$ for p ∉ ℕ (resp. for p an odd integer), every equivalent norm can be approximated uniformly on bounded sets by $C^[p]}$-smooth norms (resp. by $C^{p-1}$-smooth norms).
- Źródło:
-
Studia Mathematica; 1996, 120, 1; 61-74
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł