摘要
设{Ei:i∈I}是侧完备Riesz空间E中的一族理想,且Ei∩Ej= (i,j∈I,i≠j).文章引入理想族{Ei:i∈I}直和的概念,并给出一个表示定理.文章证明了:存在一个完备的正则Hausdorff空间X使得理想族的直和Riesz同构于C(X)其充要条件是对每个i∈I存在一个紧Hausdorff空间Xi使得EiRiesz同构于C(Xi).
Let {E_i:i∈I} be a family of infinitely many of ideals in a laterally complete Riesz space E with E_i∩E_j= (i,j∈I, and i≠j). In this paper, we introduce a definition on the direct sum of {E_i:i∈I} and show a representation theorem, which says that there exists a completely regular Hausdorff space X such that the direct sum is Riesz isomorphic to C(X) if and only if for every i∈I there exists a compact Hausdorff space X_i such that E_i is Riesz isomorphic to C(X_i).
出处
《应用泛函分析学报》
CSCD
2004年第1期39-47,共9页
Acta Analysis Functionalis Applicata
关键词
侧完备
理想
直和
Riesz同构
laterally complete
ideal
direct sum
Riesz isomorphism
