Banach空间中泛函列的一致收敛性的判定

A Decision Method of the Uniformly Convergent Functional Row in Banach Space

在Banach空间中给出了实泛函列一致收敛的概念.从泛函列表示成两个泛函的商出发,给出了一个用于判定泛函列一致收敛的定理.又由一致收敛的泛函列构造出一系列新的一致收敛的泛函列,如:一致收敛泛函列的前n项和与n的商组成的泛函列、一致收敛泛函列的前n项之积开n次方所组成的泛函列、一致收敛泛函列各项的范数组成的泛函列及一致收敛且有界的泛函列{fn(x)},{gn(x)}组成的泛函列f1(x)gn(x)+…+fn(x)g1(x)等。

This article introduced the uniformly convergent concept of functional row in the Banach space.To express from the functional row two functional business embarked,which can be used to construct uniformly convergent functional row.Also a series of new uniformly convergent functional can be constructed by the uniformly convergent functional row,for example： the quotient between sum of antecedent n items of a uniformly convergent functional row and n,the n times root of the product of uniformly convergent functional row antecedent n items,the norm of each item of a uniformly convergent functional row and the {f1（x）gn（x）＋…＋fn（x）g1（x）n} functional row from two uniformly convergent row {fn（x）,{gn（x）}} and so on.