| 引用本文： |
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林尤武,魏文展,唐献秀.局部凸空间的平均一致凸性与平均一致光滑性[J].广西科学,2009,16(1):17-22. [点击复制]
- LIN You-wu,WEI Wen-zhan,TANG Xian-xiu.Average Uniform Convexity and Average Uniform Smoothness in Locally Convex Spaces[J].Guangxi Sciences,2009,16(1):17-22. [点击复制]
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| 摘要: |
| 引进局部凸空间的平均一致凸性的概念,给出其对偶的定义,得到平均一致凸(平均一致光滑)的局部凸空间的特征刻画及其在P-自反条件下的对偶关系:(X,P)是平均一致凸(平均一致光滑)的当且仅当(X',P')是平均一致光滑(平均一致凸)的. |
| 关键词: 局部凸空间 平均一致凸性 平均一致光滑性 对偶关系 P-自反 |
| DOI： |
| 投稿时间：2008-10-21 |
| 基金项目:广西自然科学基金项目[桂科自0728050]资助 |
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| Average Uniform Convexity and Average Uniform Smoothness in Locally Convex Spaces |
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LIN You-wu1, WEI Wen-zhan2, TANG Xian-xiu1
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| (1.Department of Mathematics and Computer Science, Guangxi Teachers Education University, Nanning, Guangxi, 530023, China;2.Guangxi Economic Trade Polytechnic, Nanning, Guangxi, 530021, China) |
| Abstract: |
| The definition of average uinform converxity in locally conver spaces is introduced, and we give the definition of average uniform smoothness in locally conver spaces as the dual of average uniform converxity, and obtained some necessary and sufficient conditions of average uinform converxity (average uniform smoothness) in locally conver spaces.In addition, on the conditions of P-reflexivity, we obtained the dual relations of between average uinform converxity and average uniform smoothness, also, (X, P) is average uinform converxity (average uinform smoothness) if and only if (X', P') is average uinform smoothness (average uinform converxity). |
| Key words: locally conver spaces average uniform converxity average uniform smoothness dual theorem P-reflexivity |
