| 局部凸空间的一致凸性与一致光滑性 |
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| 引用本文： | 苏林宁.局部凸空间的一致凸性与一致光滑性[J].长江大学学报(社会科学版),1993(2). |
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| 作者姓名： | 苏林宁 |
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| 作者单位： | 宁德师专数学科 |
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| 摘 要： | 本文对局部凸空间引进一致光滑、拓扑一致光滑的概念,讨论了局部凸空间的一致凸性与一致光滑性之间的某种对偶关系,证明了:(1)若局部凸空间(E′,P~*)是一致凸的,则局部凸空间(E,P)是一致光滑的;(2)若局部凸空间(E′,P~*)是一致光滑的,则局部凸空间(E,P)是一致凸的;(3)亚完备的拓扑一致光滑的局部凸空间是半自反的.
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| 关 键 词： | 局部凸空间 强对偶 一致凸 一致光滑 拓扑一致光滑 亚完备 半自反 |
UNIFORM CONVEXITY AND UNIFORM SMOOTHNESS IN LOCALLY CONVEX SPACES |
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| Su Linning Mathematics.UNIFORM CONVEXITY AND UNIFORM SMOOTHNESS IN LOCALLY CONVEX SPACES[J].Journal of Yangtze University:Social Sciences,1993(2). |
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| Authors: | Su Linning Mathematics |
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| Institution: | Su Linning Mathematics Department of Ningde Teachers College |
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| Abstract: | In this paper,we introduce uniform smoothness in locally convex spaces and prove the following theorems:Theorem 1 If(E',P~*)is uniformly convex,then (E,P)is uniformly smooth.Theo- rem2 If (E',P~*)Pis uniformly convex,then (E,P)is uniformly convex.Here(E',P~*)is the strong topological dual space of the locally convex space(E,P). |
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| Keywords: | Iocally convex space strong topological dual uniform Convexity uniform smoothness |
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