关于无穷矩阵算子代数∑(λ,μ)的乘法连续性问题  

On the Continulty of the Multiplication of the Infinite Matrix Algebra ∑(λ,μ)

作　　者：吴从炘[1] 廖俊俊[1] 

机构地区：[1]哈尔滨工业大学系,哈尔滨150001

出　　处：《数学学报（中文版）》1999年第5期897-904,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金

摘　　要：本文对序列空间λ,μ之间的无穷矩阵算子代数∑（λ,μ）引入了16种自然的拓扑，并就这些拓补给出乘法连续性的刻划；同时，结合对∑（ω,Φ）乘法连续性的细致讨论，研究了∑（λ,μ）的乘法恒不连续的拓扑，从而全面推广并发展了[1-3]的工作．In this paper, we introduce 16 kinds of natural topologies on ∑(λ, μ), where ∑(λ,μ) denotes the algebra of the infinite matrix operators, which map the sequence space λ into another sequence space p. And we obtain a criterion for the continuity of the multiplication with respect to all kinds of topologies on ∑(λ,μ). Furthermore, with a detailed discuss of the continuity of the multiplication on ∑(ω, Ф), we study the toplogies for which the multiplication would never be continuous. As a result, the work of [1-3] is fully geneaxlized and developed.

关 键 词：无穷矩阵 拓扑代数 算子代数 乘法 连续性 

分 类 号：O177.5[理学—数学]