| 赋序列范数的矢值Banach序列空间ss(E)的凸性 |
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| 引用本文： | 任丽伟,冯国臣. 赋序列范数的矢值Banach序列空间ss(E)的凸性[J]. 数学研究及应用, 2005, 25(1): 84-91 |
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| 作者姓名： | 任丽伟 冯国臣 |
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| 作者单位： | 北京交通大学理学院数学系,北京,100044 |
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| 摘 要： | 本文对赋序列范数的矢值Banach序列空间ss(E)的一些凸性进行了讨论,得到的主要结果如下: 1.ss(E)是局部一致凸的当且仅当ss和E是局部一致凸的; 2.ss(E)是强凸的当且仅当ss和E是强凸的; 3.设ss和ss*具有AK性质,则ss(E)是非常凸的当且仅当ss和E是非常凸的.
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| 关 键 词： | 矢值序列空间 局部一致凸 强凸 非常凸 |
| 文章编号： | 1000-341X(2005)01-0084-08 |
| 收稿时间： | 2002-05-20 |
| 修稿时间： | 2002-05-20 |
Rotundity of Vector-valued Banach Squence Spaces Equipped with Sequential Norms |
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| REN Li-wei and FENG Guo-chen. Rotundity of Vector-valued Banach Squence Spaces Equipped with Sequential Norms[J]. Journal of Mathematical Research with Applications, 2005, 25(1): 84-91 |
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| Authors: | REN Li-wei and FENG Guo-chen |
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| Affiliation: | College of Science; Beijing Jiaotong University; Beijing; China;College of Science; Beijing Jiaotong University; Beijing; China |
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| Abstract: | In this paper, some convex properties of vector-valued Banach sequence spaces equipped with sequential norms are discussed. The main results are summarized as follows:1. ss(E) is locally uniformly rotund if and only if ss and E are locally uniformly rotund;2. ss(E) is strongly rotund if and only if ss and E are strongly rotund;3. Let ss and ss* have AK property, then ss(E) is very rotund if and only if ss and E are very rotund. |
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| Keywords: | vector-valued sequence space local unform rotundity strong rotundity very rotundity |
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