拟弱滴状性质与弱紧性

引入了一种新的滴状性质 ,关于局部凸空间中有界闭凸集的拟弱滴状性质 ,利用Rolewicz所引进的流动序列 ,给出了Frechet空间中有界闭凸集的拟弱滴状性质的特征 由此 ,证明了拟弱滴状性质等价于弱紧性 这样 ,Frechet空间为自反当且仅当该空间中每个有界闭凸集具拟弱滴状性质

Quasi-weak drop property and weak compactness*

We introduce a new drop property,the quasi-weak drop property for closed bounded convex sets in locally convex spaces.Using streaming sequences introduced by Rolewicz,we give a characterisation of the quasi-weak drop property for closed bounded convex sets in Frechet spaces.From this,we prove that the quasi-weak drop property is equivalent to weak compactness.Thus a Frechet space is reflexive if and only if every closed bounded convex set in the space has the quasi-weak drop property.