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Banach空间中广义正交分解定理与广义正交可补子空间
引用本文:王玉文,王辉.Banach空间中广义正交分解定理与广义正交可补子空间[J].数学学报,2001,44(6):1045-105.
作者姓名:王玉文  王辉
作者单位:1. 哈尔滨师范大学数学系
2. 哈尔滨工业大学理学院数学系
基金项目:国家自然科学基金资助项目(19971023);黑龙江省自然科学基金资助项目
摘    要:本文首先将 Hilbert空间中的Riesz正交分解定理推广到 Banach空间,得到 Banach空间广义正交分解定理.然后,利用此定理讨论由James R.C.[1]引入的Banach空间中正交概念及 Nashed M.Z.[2]引入的 Banach空间中(广义)正交可补子空间,得到判别子空间广义正交可补的充分必要条件,并由此给出Hilbert空间的一个新特征.

关 键 词:Banach空间  正交分解  正交可补  对偶映射
文章编号:0583-1431(2001)06-1045-06
修稿时间:2000年6月21日

Generalized Orthogonal Decomposition Theorem in Banach Space and Generalized Orthogonal Complemented Subspace
WANG Yu Wen.Generalized Orthogonal Decomposition Theorem in Banach Space and Generalized Orthogonal Complemented Subspace[J].Acta Mathematica Sinica,2001,44(6):1045-105.
Authors:WANG Yu Wen
Institution:WANG Yu Wen (Department of Mathematics, Harbin Normal University, Harbin 150080, P. R. China) WANG Hui (Department of Mathematics, Harbin Institute of Technology, Harbin 150080, P. R. China)
Abstract:In this paper, we have first extended Riesz orthogonal decomposition theorem in Hilbert space to Banach space and obtained generalized orthogonal decomposition theorem in Banach Space. Then, we have discussed orthogonal cencept in Banach Space introduced by James R. C1] and generalized orthogonal complemented subspace in Banach Space introduced by Nashed M. Z.2]. Finally, a sufficient and necessary condition for a subspace to be generalized orthogonal complemented and a new character of Hibert space are given.
Keywords:Banach space  Orthogonal decomposition  Orthogonal complemented  Dual mapping
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