詹华英.关于 ``Banach spaces failing the almost isometric universal extension property'' 的一个注记[J].数学研究及应用,2008,28(3):613~616 |
关于 ``Banach spaces failing the almost isometric universal extension property'' 的一个注记 |
A Note of Paper ``Banach Spaces Failing the Almost Isometric Universal Extension Property" |
投稿时间:2006-06-22 修订日期:2007-01-17 |
DOI:10.3770/j.issn:1000-341X.2008.03.022 |
中文关键词: 有常数$\alpha$的性质${\cal A}$ 凸性模 $\lambda$-EP $\lambda$-UEP. |
英文关键词:property ${\cal A}$ with constant $\alpha$ modulus of convexity $\lambda$-EP $\lambda$-UEP. |
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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中文摘要: |
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. |
英文摘要: |
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 $\alpha \in[0,1)$. In this paper, we give a sufficient condition for a Banach space to have property ${\cal A}$ with constant $\alpha \in[0,1)$, and some remarks on Speegle's paper [1]. |
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