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。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。