| 关于 ``Banach spaces failing the almost isometric universal extension property' 的一个注记 |
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| 引用本文： | 詹华英.关于 ``Banach spaces failing the almost isometric universal extension property'' 的一个注记[J].数学研究与评论,2008,28(3):613-616. |
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| 作者姓名： | 詹华英 |
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| 作者单位： | 天津工业大学理学院, 天津 300384; 南开大学数学科学学院, 天津 300017 |
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| 基金项目： | 国家自然科学基金(No.10571090);高等学校博士点资助项目(No.20060055010);天津市教育委员会科研基金(No.20060402). |
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| 摘 要： | D.M. Speegle 在文献1] 中给出了具有常数 $\alpha$的性质${\cal A}$ 的定义,并且证明了任意无限维的可分一致光滑Banach空间都具有这样的性质,而且常数 $\alpha\in 0,1)$.本文给出了一个使得无限维可分Banach空间具有这种性质的充分条件,以及几个关于文献1] 的注解.
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| 关 键 词： | 有常数$\alpha$的性质${\cal A}$ 凸性模 $\lambda$-EP $\lambda$-UEP. |
| 收稿时间： | 2006/6/22 0:00:00 |
| 修稿时间： | 2007/1/17 0:00:00 |
A Note of Paper ``Banach Spaces Failing the Almost Isometric Universal Extension Property" |
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| ZHAN Hua Ying.A Note of Paper ``Banach Spaces Failing the Almost Isometric Universal Extension Property"[J].Journal of Mathematical Research and Exposition,2008,28(3):613-616. |
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| Authors: | ZHAN Hua Ying |
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| Institution: | College of Science, Tianjin University of Technology, Tianjin 300384, China;School of Mathematics, Nankai University, Tianjin 300017, China |
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| Abstract: | The definition of property ${\cal A}$ with constant $\alpha$ was introduced by D. M. Speegle, who proved that every infinite dimensional separable uniformly smooth Banach space has property ${\cal A}$ with constant $\alpha \in0,1)$. In this paper, we give a sufficient condition for a Banach space to have property ${\cal A}$ with constant $\alpha \in0,1)$, and some remarks on Speegle's paper 1]. |
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| Keywords: | property ${\cal A}$ with constant $\alpha$ modulus of convexity $\lambda$-EP $\lambda$-UEP |
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