| 局部β-凸空间中的第二分离性定理及其共轭锥上的有界性定理 |
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| 引用本文： | 王见勇,马玉梅. 局部β-凸空间中的第二分离性定理及其共轭锥上的有界性定理[J]. 数学研究及应用, 2002, 22(1): 25-34 |
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| 作者姓名： | 王见勇 马玉梅 |
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| 作者单位： | 1. 常熟高等专科学校数学系,江苏常熟215500
2. 大连大学数学系,辽宁大连116622 |
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| 摘 要： | 第一部分给出局部β－凸空间中的第二分离性定理和Ｍｉｎｋｏｗｓｋｉ定理及Ｋｒｅｉｎ－Ｍｉｌｍａｎ定理等；第二部分得到其共轭锥上Ｕ Ｆ－有界与Ｕ Ｂ－有界等价的充要条件为原空间是次完备的．
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| 关 键 词： | locally β-convex space β-subseminorm β-extreme point（set） β-Minkowski functional conjugate （topological） cone subcomplete U F - （U B- ）boundedness. |
| 收稿时间： | 1998-12-22 |
The Second Separation Theorem in Locallyβ-Convex Spaces and the Boundedness Theorem in Its Conjugate Cones |
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| WANG Jian-yong and MA Yu-mei. The Second Separation Theorem in Locallyβ-Convex Spaces and the Boundedness Theorem in Its Conjugate Cones[J]. Journal of Mathematical Research with Applications, 2002, 22(1): 25-34 |
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| Authors: | WANG Jian-yong and MA Yu-mei |
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| Affiliation: | Dept. of Math.; Changshu College; Jiangsu; China;Dept. of Math.; Dalian University; Liaoning; China |
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| Abstract: | This paper deals with the locally β-convex analysis that generalizes the locally convex analysis. The second separation theorem in locally β-convex spaces, the Minkowski theorem and the Krein-Milman theorem in the β-convex analysis are given.Moreover, it is obtained that the UF-boundedness and the UB-boundedness in its conjugate cone are equivalent if and only if X is subcomplete. |
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| Keywords: | conjugate (topological) cone subcomplete UF - (UB-)boundedness |
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