期刊信息
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- 刊名: 河北师范大学学报(自然科学版)Journal of Hebei Normal University (Natural Science)
- 主办: 河北师范大学
- ISSN: 1000-5854
- CN: 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
关于可闭的K-正定算子方程的注记
-
1. 军械工程学院, 应用数学研究所, 河北, 石家庄, 050003;
2. 河北金融学院, 基础部, 河北,保定, 071000 -
DOI:
Note on Closed of K-positive Definite Operator Equations
摘要/Abstract
摘要:
设X为任意Banach空间,X*为其共轭空间,A:D(A)X→X*为可闭的K-正定算子,D(A)=D(K),则存在常数α>;0使得x∈D(A),有‖Ax‖≤α‖Kx‖,而且A为闭算子,R(A)=X*,f∈X*,方程Ax=f有唯一解。
Abstract:
Let X be an arbitrary Banach space with a dual X and let A:D(A)X→X* be a K-positive definite operator with D(A)=D(K).Then there exists a constant α>0 such that ‖Ax‖≤α‖Kx‖,for all x∈D(A).Furthermore,the operator A is closed,R(A)=X and the equation Ax=f,for each f∈X*,has a unique solution.In the case X is a Hilbert space,a constructive solvability for the equation Ax=f,for each f∈H,is also given.
关键词
关键词:
任意Banach空间
;
K-正定算子
;
可解性
Key words:
arbitrary Banach space
;
K-positive definite operator
;
solvability