On Asymptotically Isometric Copies of $l^{\beta} (0<\beta<1)$

DOI：10.3770/j.issn:1000-341X.2010.06.011

 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

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.

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.