序列弱收敛的特征

THE CHARACTER OF THE WEAKLY CONVERGENT SEQUENCE

本文在Schauder基存在的假设下,讨论了Banach空间中序列弱收敛的性质,自反Banach空间中序列弱收敛的等价条件,给出了Banach空间中序列弱收敛与强收敛等价的一个充分条件。

In this paper, on the assumption that X is a Banach space with Schauder basis, the properties of a weakly convergent sequence is discussed. An equivalent condition for a sequence being weakly convergent is given whenever X is also reflexive. We also give a sufficient condition for a weakly convergent sequence to be strongly convergent,