| 对巴拿赫空间理论中两个定理的新证明 |
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| 引用本文： | 张清年,吴慧莲. 对巴拿赫空间理论中两个定理的新证明[J]. 河北工程大学学报(自然科学版), 2005, 22(2): 111-112 |
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| 作者姓名： | 张清年 吴慧莲 |
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| 作者单位： | 河北工程学院,理学院,河北,邯郸,056038;河北工程学院,理学院,河北,邯郸,056038 |
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| 摘 要： | 在巴拿赫空间理论中,Hahn-Banach泛函延拓定理作为泛函分析三大基本定理之一,分隔性定理是Hahn-Banach定理的重要应用,本文利用"超平面"的方法,改进了一个分隔性定理的证明;另外,本文利用邻域的"平移"方法,给出了定义在赋范线性空间内的凸集上的次凸泛函连续性的简捷证明。
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| 关 键 词： | 赋范线性空间 线性泛函 次凸泛函 超平面 邻域平移 |
| 文章编号： | 1007-6743(2005)02-0111-02 |
| 修稿时间： | 2005-01-21 |
New proofs of two basic theorems in Banach Space |
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| ZHANG Qing-nian,WU Hui-lian. New proofs of two basic theorems in Banach Space[J]. Journal of Hebei University of Engineering(Natural Science Edition), 2005, 22(2): 111-112 |
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| Authors: | ZHANG Qing-nian WU Hui-lian |
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| Abstract: | In the theory of Banach Space,Hahn-Banach extension theorem is well known as one of three basic theorems of Banach Space and the separation theorem is one important applieation.In this paper,making use of hyperplane method,we improve the proof of the separation theorem;On the other hand,we use a new method of moving neighborhood to simplify the proof for the continuity of a subconvex function defined on a convex in a normed linear space. |
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| Keywords: | normed linear space linear function subconvex function hyperplane moving neighborhood |
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