- Tytuł:
- Weak nearly uniform smoothness of the \(\psi\)-direct sums \((X_1 \oplus \dots\oplus X_N)_\psi\)
- Autorzy:
-
Kato, Mikio
Tamura, Takayuki - Powiązania:
- https://bibliotekanauki.pl/articles/746388.pdf
- Data publikacji:
- 2012
- Wydawca:
- Polskie Towarzystwo Matematyczne
- Tematy:
-
absolute norm
convex function
\(\psi\)-direct sum of Banach spaces
weak nearly uniform smoothness
Garcı́a-Falset coefficient
Schur property
fixed point property - Opis:
- We shall characterize the weak nearly uniform smoothness of the \(\psi\)-direct sum \((X_1\oplus \dots\oplus X_N)_\psi\) of \(N\) Banach spaces \(X_1,\dots,X_N\), where \(\psi\) is a convex function satisfying certain conditions on the convex set \(\Delta_N = \{(s_1 ,\dots , s_{N-1})\in \mathbb{R}_+^{N-1} : \sum_{i=1}^{N-1} s_i \leq 1\). To do this a class of convex functions which yield \(\ell_1\)-like norms will be introduced. We shall apply our result to the fixed point property for nonexpansive mappings (FPP). In particular an example will be presented which indicates that there are plenty of Banach spaces with FPP failing to be uniformly non-square.
- Źródło:
-
Commentationes Mathematicae; 2012, 52, 2
0373-8299 - Pojawia się w:
- Commentationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł