【摘要】 本文就可分Banach空间中元素的最小序列(也称双直交序列)可以扩充到在全空间中完备这一事实,说明在空间不可分情况下,对于由不可数个元素组成的所谓最小系,这种完备性扩充未必可行.此外,还应用最小序列扩充性质给出可分的遗传不可分解空间的一个特征刻画.更多还原

【Abstract】 In this paper it is shown that the problem of extensions of complete minimal sequences in separable Banach spaces has an affirmative answer. We give two examples in X = l∞ to show that corresponding results do not hold for minimal systems in nonseparable Banach spaces. In addition, a characterization of hereditarily indecomposable Banach spaces is given in terms of the properties of the extension of minimal sequences.更多还原