Banach空间的p-弱近似性质

p-Weak Approximation Property in Banach Spaces

给出了Banach空间的p-弱近似性质和p-有界弱近似性质的定义,获得了这些性质的一些刻画.利用这些刻画证明了如果一个Banach空间X的对偶空间X＊有p-弱近似性质（或p-有界弱近似性质）,则X有p-弱近似性质（或p-有界弱近似性质）,在一般情况下反之不成立。

In this paper, the authours introduce the definitions of the p-weak approximation property and the p-bounded weak approximation property in Banach spaces, and derive some characterizations of these properties. They show that if the dual of a Banach space X has the p-weak approximation property （or the p-bounded weak approximation property）, then X itself has the p-weak approximation property （or the p-bounded weak approximation property）. The converse is not true in general.