摘要
Ｘ为自反、严格凸Ｂａｎａｃｈ空间，Ｌ为Ｘ中闭子空间，Ｐ：Ｘ→Ｌ为单值算子，该文给出Ｐ成为Ｌ上度量投影ＰＬ的判据及ＰＬ为线性算子的充分必要条件．在自反Ｂａｎａｃｈ空间中，利用对偶映射，给出超平面上（集值）度量投影的表达式．对于自反、严格凸、光滑的Ｂａｎａｃｈ空间中线性流形上的（单值）度量投影，利用广义右逆的表示，求出其表达式．在后继文章中将给出此表达式的应用．
Let X be a Banach space. L X , the closed subspace. A character for a opera-tor from X to L to be a metric projection of L is given in this paper. A representive of single value metric projection on the linear manifold in the reflexive. smooth.strictly convex Ba-nach space X is given by means of GI of the linear operator, so is for the representive of set value projection in the reflexive Banach space X by dual mapping of X. Application of rep-resentive will be given in the following papers.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2001年第1期29-35,共7页
Acta Mathematica Scientia
基金
国家自然科学基金
黑龙江省自然科学基金资助
