| 包含$l^{beta}(0 |
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| 引用本文： | 智琛,宋眉眉. 包含$l^{beta}(0
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| 作者姓名： | 智琛 宋眉眉 |
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| 作者单位： | 天津理工大学理学院, 天津 300384;天津理工大学理学院, 天津 300384 |
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| 基金项目： | 天津市教委科技基金(Grant No.20060402). |
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| 摘 要： | Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L（X,Y） fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L（X,Y）.
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| 关 键 词： | asymptotically isometric copy space of bounded linear operators quotient space fixed point property. |
| 收稿时间： | 2009-04-28 |
| 修稿时间： | 2010-05-28 |
Asymptotically Isometric Copy of $l^{beta}~(0 |
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| Chen ZHI and Mei Mei SONG. Asymptotically Isometric Copy of $l^{beta}~(0
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| Authors: | Chen ZHI and Mei Mei SONG |
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| Affiliation: | Department of Mathematics, Tianjin University of Technology, Tianjin 300384, P. R. China;Department of Mathematics, Tianjin University of Technology, Tianjin 300384, P. R. China |
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| Abstract: | Assume $X$ is a normed space, every $x^{ast}in S(X^{ast})$ can reach its norm at some point in $B(X)$, and $Y$ is a $beta$-normed space. If there is a quotient space of $Y$ which is asymptotically isometric to $l^{beta}$, then $L(X,Y)$ contains an asymptotically isometric copy of $l^{beta}$. Some sufficient conditions are given under which $L(X,Y)$ fails to have the fixed point property for nonexpansive mappings on closed bounded $beta$-convex subsets of $L(X,Y)$. |
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| Keywords: | asymptotically isometric copy space of bounded linear operators quotient space fixed point property. |
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