| 局部凸空间的一致极凸性与一致极光滑性 |
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| 引用本文： | 陈利国,罗成.局部凸空间的一致极凸性与一致极光滑性[J].内蒙古大学学报(自然科学版),2009,40(6). |
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| 作者姓名： | 陈利国 罗成 |
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| 作者单位： | 1. 内蒙古财经学院统计与数学学院,呼和浩特,010051
2. 内蒙古大学数学科学学院,呼和浩特,010021 |
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| 基金项目： | 内蒙古自然科学基金资助项目 |
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| 摘 要： | 设X是一个实线性空间,P是X上的一可分离的半范数族,(X,T_P)表示由P生成的局部凸空间,(X,P)为一个偶对.引入偶对(X,P)为一致极凸和一致极光滑的概念,并证明它们具有对偶关系,讨论了与其它几种凸性(光滑性)之间的关系,另外,在P-自反的条件下给出它们之间的对偶定理,从而推广了Banach空间相应概念和结果.
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| 关 键 词： | 一致极凸性 一致极光滑性 偶对 |
Uniformly Extreme Convexity and Uniformly Extreme Smoothness in Locally Convex Spaces |
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| CHEN Li-guo,LUO Cheng.Uniformly Extreme Convexity and Uniformly Extreme Smoothness in Locally Convex Spaces[J].Acta Scientiarum Naturalium Universitatis Neimongol,2009,40(6). |
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| Authors: | CHEN Li-guo LUO Cheng |
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| Institution: | CHEN Li-guo1,LUO Cheng2(1.School of Statistics and Mathematics,Inner Mongolia Finance and Economics College,Hohhot 010051,China,2.School of Mathematial Sciences,Inner Mongolia University,Hohhot 010021,China) |
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| Abstract: | Let X be a real linear space,P be a family of separated seminorms on X,(X,T_P) denote the locally convex space generated by P,and the dual (X,P) denote the space X that has the topolopy T_P generated by the seminorm family P.The notions of uniformly extreme convex and uniformly extreme smooth for dual (X,P) are introduced,and their dual relationship is proved.The relationship with the other convexity (smoothness) are discussed.In addition,on the conditions of P-reflexivity,the dual theorem between uniformly extreme convexity and uniformly extreme smoothness is obtained,and thus the notions and results are generalized in Banach spaces. |
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| Keywords: | uniformly extreme convexity uniformly extreme smoothness dual |
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