| 局部β-凸空间的共轭锥与Hahn-Banach定理 |
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| 引用本文： | 王见勇. 局部β-凸空间的共轭锥与Hahn-Banach定理[J]. 数学的实践与认识, 2002, 32(1): 143-149 |
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| 作者姓名： | 王见勇 |
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| 作者单位： | 常熟高等专科学校数学系,江苏,215500 |
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| 摘 要： | 由 [1 ],局部β-凸空间 X的共轭锥 X*β 取代共轭空间在局部β-凸分析中扮演核心角色 .本文第一部分在局部β-凸空间上给出β-次半范的 Hahn-Banach定理 ,第二部分通过共轭锥 ( X*β ,‖‖ )得到赋β-范空间 ( X,‖‖β)的可分性定理 ,第三部分给出局部 β-凸空间的共轭锥 X*β 在一致收敛拓扑下的完备性定理等 .
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| 关 键 词： | 局部β-凸空间 β-次半范 (赋范)共轭锥 拟平移不变拓扑锥 内覆盖 |
| 修稿时间： | 2001-09-11 |
The Conjugate Cones of Locallyβ-Convex Spaces and the Hahn-Banach Theorem |
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| WANG Jian-yong. The Conjugate Cones of Locallyβ-Convex Spaces and the Hahn-Banach Theorem[J]. Mathematics in Practice and Theory, 2002, 32(1): 143-149 |
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| Authors: | WANG Jian-yong |
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| Abstract: | By , the conjugate cone X * β of a locally β-convex space plays a key role in β-convex analysis. In the first part of this aper, we prove the Hahn-Banach theorem about β-subseminormes. In the secoind, by way of the normed conjugate cone (X * β,‖‖), we give the separability theorem of a β-normed space (X,‖‖ β). We show the completeness of conjugate cone X * β of a locally β-convex space for the uniformly convergent topology at last. |
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| Keywords: | locally β-convex space β-subseminorme (normed) conjugate cone quasi-translation invariant topological cone interior covering |
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