| Asymptotically Isometric Copy of $l^{\beta}~(0<\beta<1)$ in Spaces of Bounded Linear Operators |
| Received:April 28, 2009 Revised:May 28, 2010 |
| Key Words:
asymptotically isometric copy space of bounded linear operators quotient space fixed point property.
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| Fund Project:Supported by the Science and Technology Foundation of Educational Committee of Tianjin (Grant No.20060402). |
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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 $L(X,Y)$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.03.023 |
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