数学方法：线性代数，赋范空间，分布，积分。
Mathematical Methods: Linear Algebra, Normed Spaces, Distributions, Integration.
给出了线性赋范空间中球的几个平移性质及其应用。
In this paper, some properties of translation and application for ball in normed linear space are given.
关于完备随机赋范模为随机自反空间的特征化定理；
Part 4 to characterizations for a complete random normed module to be random reflexive;
证明了模糊赋范空间上有界线性算子的一个保范延拓定理。
Naught space properties of compact linear operator in normed space;
最后，证明了在一些经典赋范空间中对称性的双正交元存在。
Finally, the existence of symmetry biorthogonal elements in some classical normed Spaces is proved.
本文证明了赋范线性空间中有界齐性算子与在零点连续的齐性算子等价。
In this paper, the equivalent relation of boundedness and continuity at zero for homogeneous operator in normal linear space is proved.
随机赋范空间中的共鸣定理将可能成为随机泛函分析与概率论的新应用工具。
The random principle of uniform boundedness will be also to devoted to the possible of applications of random functional analysis and probability theory, as a new tool.
给出了赋范共轭空间的点与(紧)凸集、紧凸集之间被原空间中的点分隔的定理。
It is shown that a point and a (compact) convex set are separated in this paper, and two compact convex sets are separated by a point of the original space in normed dual space.
本文讨论了利用线性赋范空间中已知的几种正交性概念来给出内积空间的某些特征。
In this paper we have discussed the characterizations of inner product Spaces by using several different concepts of orthogonality in normed linear Spaces which have been given by various authors.
本文给出2 -赋范空间一致凸、一致正规结构、正规结构概念，指出这类空间具有不动点性质。
This paper introduces the concepts of uniform convex, uniformly normal structure and normal structure for 2-normed Spaces. It is proved that for such Spaces, the fixed point property holds.
而对几乎处处极限定理和自赋范极限理论的研究则是近几十年来概率极限理论研究中的两个重要方向。
The almost sure central limit theorem and self-normalized limit theory have become two important fields of the study of probability limit theory in recent decades.
本文指出了赋范线性空间上的一些局部凸拓扑的完备性与它的单位球上相应的诱导拓扑的完备性之间的关系。
The relation between the completeness of several local convex topology in normed vector space and that of induction topology of its unit ball was pointed out in this paper.
摘要研究一类模糊范数及其层次结构性质，对模糊赋范空间的层次空间的完备性、分离性等性质进行了讨论。
This paper studies a fuzzy norm and its stratified properties. the completeness and separability of stratified space of fuzzy normed space are discussed.
存在不完备的广义模糊赋范空间。结论说明赋范空间中的一些概念和结果可类似的在广义模糊赋范空间中建立。
Conclusion It has been shown that some concepts and results in a normed space can be similarly established in a generalized fuzzy normed space.
本文的目的是把增生映象的概念推广到概率赋范空间，并研究具增生映象的方程在概率赋范空间中解的存在性条件。
The purpose of this paper is to expand the concept of accretive mapping to probabilistic normed spaces and to study the existence conditions of solutions for the accretive mapping equations.
在赋范空间几何学的研究中，一个潜在的主题就是在更为一般的空间中寻找一个新的概念来替代欧式空间中的正交性。
During studying the geometry of normed Spaces, a potential subject is looking for a new concept in more general Spaces to replace the concept of orthogonality in Euclidean space.
本文证明了在一定条件下赋范线性空间与其共轭空间的单位球面之间的等距算子可以延拓为全空间的实线性等距算子。
In this paper, we show that the isometry between the unit spheres of certain normed space and its dual space can be extended to a real linear isometry on the whole space.
把计算方法中的最小二乘法与泛函的抽象空间联系起来，得到最佳逼近问题的抽象提法，并在赋范线性空间探讨最小二乘法。
This article focuses on the topics that by connecting the the least-squares Minimization with the functional abstract space, the abstract definition of the best approximation problem is abtained.
表示出了一类赋准范空间的随机对偶空间，并证明这类赋准范空间之间，几乎处处有界线性算子所组成空间的完备性。
The random dual Spaces of a class of quasi-normed Spaces is given. The completeness of the Spaces having bounded operators all most everywhere has also been proved.
表示出了一类赋准范空间的随机对偶空间，并证明这类赋准范空间之间，几乎处处有界线性算子所组成空间的完备性。
The random dual Spaces of a class of quasi-normed Spaces is given. The completeness of the Spaces having bounded operators all most everywhere has also been proved.
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