On Asymptotically Isometric Copies of $l^{\beta} (0<\beta<1)$ |
Received:December 09, 2008 Revised:September 15, 2009 |
Key Words:
asymptotically isometric copy $\beta$-normed space $\beta$-absolutely homogeneous.
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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: |
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. |
Citation: |
DOI:10.3770/j.issn:1000-341X.2010.06.011 |
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