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 |
赋序列范数的矢值Banach序列空间ss(E)的凸性 |
Rotundity of Vector-valued Banach Squence Spaces Equipped with Sequential Norms |
投稿时间:2002-05-20 |
DOI:10.3770/j.issn:1000-341X.2005.01.012 |
中文关键词: 矢值序列空间 局部一致凸 强凸 非常凸 |
英文关键词:vector-valued sequence space local unform rotundity strong rotundity very rotundity |
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中文摘要: |
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. |
英文摘要: |
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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