| 智琛,宋眉眉.关于含渐近等距于$l^{\beta}(0<\beta<1)$子空间的赋$\beta$范空间[J].数学研究及应用,2010,30(6):1032~1038 |
| 关于含渐近等距于$l^{\beta}(0<\beta<1)$子空间的赋$\beta$范空间 |
| On Asymptotically Isometric Copies of $l^{\beta} (0<\beta<1)$ |
| 投稿时间：2008-12-09 修订日期：2009-09-15 |
| DOI：10.3770/j.issn:1000-341X.2010.06.011 |
| 中文关键词: 渐近等距翻版 赋$\beta$范空间 $\beta$-绝对齐性. |
| 英文关键词:asymptotically isometric copy $\beta$-normed space $\beta$-absolutely homogeneous. |
| 基金项目:天津市教委科技基金项目(Grant No.20060402). |
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| 中文摘要: |
| 当一个赋$\beta$范空间包含$l^{\beta}$的渐近等距copy时,我们给出了其上非负,次加,$\beta$-绝对齐性,连续泛函全体的刻画.并且,证明了如果一个赋$\beta$范空间的有界闭,$\beta$-凸子集$K$包含渐近等距于$l^{\beta}$的基的序列,那么$K$包含一个闭, $\beta$-凸子集,其不具有不动点性质. |
| 英文摘要: |
| We get the characterizations of the family of all nonnegative, subadditive, $\beta$-absolutely homogeneous and continuous functionals defined on $X$, when the $\beta$-normed space $X$ contains an asymptotically isometric copy of $l^{\beta}$. Moreover, it is proved that if a closed bounded $\beta$-convex subset $K$ of a $\beta$-normed space contains an asymptotically isometric $l^{\beta}$-basis, then $K$ contains a closed $\beta$-convex subset $C$ which fails the fixed point property. |
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