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| 摘要: |
| 本文研究了ω-非常凸空间和ω-非常光滑空间的问题. 利用局部自反原理和切片证明了ω-非常凸空间和ω-非常光滑空间的对偶关系, 讨论了ω-非常凸空间和ω-非常光滑空间与其它凸性和光滑性的关系, 给出了ω-非常凸空间与ω-非常光滑空间的若干特征刻画, 所得结果完善了关于Banach 空间凸性与光滑性理论的研究. |
| 关键词: ω-非常凸 ω-非常光滑 切片 |
| DOI： |
| 分类号:O177.2 |
| 基金项目:国家自然科学基金资助项目(11061022);内蒙古自然科学基金资助项目(2012MS1022);内蒙古师范大学人才培养基金资助项目(RCPY-2-2012-K-034). |
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| ω-VERY CONVEX SPACES AND ω-VERY SMOOTH SPACES |
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ZENG Chao-ying,SUYA La-tu
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| Abstract: |
| In this article, we study the problems of about ω-very convex spaces and ω-very smooth spaces. Using the local reflexive principle and the slice of unit sphere, we show that the ω-very convex spaces and ω-very smooth spaces are dual notions and study the relation between ω-very convexity, ω-very smoothness with various convexity and smoothness, and give some characteristic descriptions of ω-very smoothness and ω-very convexity . These results perfect the research on convexity and smoothness about Banach spaces. |
| Key words: ω-very convexity ω-very smoothness slice |
