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  最后修改时间: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).
作者单位
智琛 天津理工大学理学院, 天津 300384 
宋眉眉 天津理工大学理学院, 天津 300384 
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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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