中文摘要：

设X是Banach空间,Y为X的子空间,BX,BY分别是X和Y的闭单位球.本文研究BY的逼近紧性,证明了BY在X中是逼近紧的当且仅当对Y的每个与BX相交的平移YT,YT∩BX在YT中都是逼近紧的.还得到BY逼近紧的稳定性结果.

英文摘要：

Let Y be a subspace of a Banach space X,BX,BY be the closed unit ball of X and Y respectively.We investigate the approximative compactness of BY.We prove that BY is approximative compact in X if and only if for every translation YT of Y with YT ∩ BX≠⊙,YT ∩ BX is approximative compact in YT.We also obtain the stability result of the approximative compactness of BY.