Using the ultrapowers as an implement, the mutual reflection of the properties of Banach spaces and its separable subspaces is discussed.
利用超幂这一工具讨论了 Ｂａｎａｃｈ 空间上的一些性质与其可分子空间上性质的相互体现，给出了超自反空间的一个等价命题。
Some new concepts are introduced such as power hyperlattice,trivial power hyperlattice and single-point power hyperlattice.
引入了幂超格的概念并讨论了其相关性质,给出了平凡幂超格和单点幂超格的概念。
A series of properties of power hyperlattice are discussed.
对幂超格的性质进行了研究。
This paper gives simple necessary and sufficient conditions for convergence of Neumann type expansion and the expressions of its limit matrix,and corrects the wrong conclusions on the convergence condition and the limit matrix of hyperpower iteration in Ref[1].
给出了Neumann型级数 ∞j=0(I -X0 A) jX0 收敛的较简单的充要条件与极限矩阵的多种表达式 ,并纠正了文 [1 ]中关于p阶超幂迭代Xk+ 1 =[ p- 1j=0(I-XkA) j]Xk收敛的充要条件与极限矩阵表达式的不正确结论 ,还讨论了相关的若干问
Without assuming the k(x,y,u)≥0(x,y∈G,u∈[0,+∞)),that every real number in some two symmetrical infinite interval about the origin is an eigenvalue of Урысон operator of the ultrapower type are obtained.
不设函数k(x,y,u)≥0(x,y∈G,u∈[0,+∞)),对於超幂型Урысон算子得出某种关於原点对称的两个无穷区间中的每一个实数皆为它的固有值。