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.  
Fund Project:Supported by the Science and Technology Foundation of Educational Committee of Tianjin (Grant No.20060402).
Author NameAffiliation
Chen ZHI Department of Mathematics, Tianjin University of Technology, Tianjin 300384, P. R. China 
Mei Mei SONG Department of Mathematics, Tianjin University of Technology, Tianjin 300384, P. R. China 
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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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