弱Hahn-Banach光滑Banach空间的一个特征性质(英文)

A CHARACTERIZATION OF THE WEAKLY HAHN-BANACH SMOOTH BANACH SPACES

本文证明了,Banch空间X是弱Hahn-Banach光滑的当且仅当对于任何网{x_α~*}(?)S~*,如果x_α~*(x)→1(x∈S),那么{x_α~*}有弱收敛的子网。

In this paper, we show that a Banach space X is weakly Hahn-Banach smooth if and only if for any net {x_α~*}(?)S~* satisfying x_α~*(x)—→1(x∈S),{x_α~*} has a weakly convergent subnet.