n个无穷维闭子空间直和的等价描述  

The Equivalent Descriptions for the Direct Sum of n Infinite Dimensional Closed Subspaces

作　　者：张云南[1] 张文[2] 

机构地区：[1]福建师范大学数学与计算机科学学院,福建福州350007 [2]厦门大学数学科学学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2010年第6期769-771,共3页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金资助项目(10926173);福建省自然科学基金资助项目(2009J05002)

摘　　要：作为Banach空间中2个无穷维闭子空间(拓扑)直和的等价描述的推广,给出Banach空间中n个无穷维闭子空间(拓扑)直和的等价描述,将有助于HDn空间与QDn空间的深入研究.同时,还详细分析并举例说明一些2个无穷维闭子空间(拓扑)直和的等价描述不能推广到n个无穷维闭子空间(拓扑)直和的原因.As a promotion of the equivalent descriptions for the direct sum of 2 infinite dimensional closed subspaces,this paper gave some equivalent descriptions for the direct sum of n infinite dimensional closed subspaces.This will contribute to the further research of HDn spaces and QDn spaces.At the same time,this paper also detailedly analyzed and illustrated by giving examples the reasons why some equivalent descriptions for the direct sum of 2 infinite dimensional closed subspaces can not be promoted to the case of the direct sum of n infinite dimensional closed subspaces.

关 键 词：BANACH空间 代数直和 拓扑直和 

分 类 号：O177.2[理学—数学]