乘积Riesz空间的收敛性质

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中图分类号：0177.92 文献标识码：A 文章编号：1674-0033(2025)06-0013-04

Convergence Properties of the Product Riesz Spaces

LIU Yan-Li, CHENG Na (College of Science,Xihua University,Chengdu 61oo39,Sichuan)

Abstract:Let be a family of Riesz space and be the product of Riesz spaces,the relationship between convergent sequences in product Riesz spaces and their factor spaces are studied. It is shown that relatively uniformly convergent sequences in the product Riesz space maintain their linearity and lattice - order properties when projected onto the factor spaces.Furthermore,necessary and sufficient conditions are established for the existence of a u -uniform limit for every monotone u -uniform Cauchy sequence in an Archimedean product Riesz space E

Key words: product Riesz space; factor space; convergence property; order complete

在Riesz空间理论中，经常涉及到三个重要的收敛性：序收敛、 u- 一致收敛和相对一致收敛，它们在Banach格及算子的研究中起着重要作用[-。（剩余15005字）