无穷矩阵

At first, it presents a survey of the studyhistory as well as present situation in the λ-multiplier convergent series,invariant, infinite matrix algebras, Schur-matrices and p-uniform Toeplitzmatrices and the Eberlein-Smulian theorem, etc.

本文共5章。首先回顾了〓数乘收敛级数、不变性、无穷矩阵代数、Schur—矩阵与p-一致Toeplitz矩阵以及Eberlein-Smulian定理等的研究历史和现状。

It investigates mainly the dualinvariant of λ- multiplier convergent series, the full invariant ofλ-multiplier convergent series, the λ- multiplier convergent series in spaceswith a basis, the compact sets in the infinite matrix topological algebras, thecharacteristics of have the same compact sets in different topologies,the weak sequentially completeness of , the characteristics ofSchur-matrices, the characteristics of p- uniform Toeplitz matrices and theEberlein-Smulian theorem in the locally convex spaces, etc.

主要研究了〓数乘收敛级数的对偶不变性，〓数乘收敛级数的全程不变性，有基空间中的〓数乘收敛级数，无穷矩阵拓扑代数〓中的紧集，〓在不同拓扑下具有相同紧集的刻划，〓的弱序列完备性，Schur—矩阵的刻划，p-一致Toeplitz矩阵的刻划以及局部凸空间上的Eberlein—Smulian定理等。

At first,it presents a survey of over 80 years'study of the infinite matrix theory and the study history as well as present situation in thespace structure theory related to this paper.

首先回顾了无穷矩阵理论研究80多年来的主要阶段、主要成果以及空间结构理论中与本文相关联方面的研究历史和现状。

On the infinite matrix transformations and convergence,first,it presents an equiva-lent form of the famous Antosik-Mikusinski basic matrix theorem.

在无穷矩阵变换与收敛方面，首先指出著名的Antosik-Mikusinski基本矩阵定理的一个等价形式。

On the characterizations of spaces by the infinite matrix methods,let E be a topo-logical vector space,if for each 〓 and 〓,there is a sequence 〓 in A suchthat 〓.Then E is said to be a sequential topological vector space.

在无穷矩阵方法对空间的刻划方面，设E是一个拓扑向量空间，若对每个〓一定存在A中序列〓使得〓，那么称E是一个序列型拓扑向量空间。

By using theconvergence properties of infinite matrix in E and the sequentially open sets notion,it pr-esents a criterion for the sequential topological vector spaces.

本文首先借助于E中无穷矩阵的收敛性态及序列开集概念给出了E是序列型空间的刻划。

For the analysis properties of infinite matrix,first,it establishes the automatic conti-nuity theorems on the sequence spaces with 0-GHP or WGHP,and the automaticboundedness theorem on the sequence spaces with 0-GHP.

在无穷矩阵的分析性质方面，建立了具有0-GHP或具有WGHP的矢值序列空间上无穷矩阵算子的自连续性定理，以及具有0-GHP矢值序列空间上无穷矩阵算子的自有界性定理。

It investigates mainly infinite matrix conver-gence、infinite matrix transformations、the automatic continuity and boundedness of infinitematrix operators、infinite matrix topological algebras、invariant theory、infinite matrix meth-ods、compact operators series and Eberlein-Smulian theorem,etc.

主要研究了无穷矩阵收敛、无穷矩阵变换、无穷矩阵算子的自连续性和自有界性、无穷矩阵拓扑代数、不变性理论、无穷矩阵方法、紧算子级数与Eberlein-Smulian定理等。

Then,it notices that all infi-nite matrix operators between the sequence spaces with the WGHP may form a topologicalalgebra.It also studies the weak sequentially completeness of this class of topological al-gebras and some other basic properties.

其次发现了具有WGHP序列空间上无穷矩阵算子所成之拓扑代数，并研究了这类无穷矩阵拓扑代数的弱序列完备性等一些基本性质。

Then,it introduces theabstract 〓-WGHP and finitely quasi 〓-families and establishes two basic convergencetheorems on them.

其次引进了具有〓的抽象序列族以及抽象的有限拟〓族，并建立了其上无穷矩阵收敛的等价条件。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。