We get the characterizations of the family of all nonnegative,subadditive,β-absolutely homogeneous and continuous functionals defined on X,when the β-normed space X contains an asymptotically isometric copy of lβ.Moreover,it is proved that if a closed bounded β-convex subset K of a β-normed space contains an asymptotically isometric lβ-basis,then K contains a closed β-convex subset C which fails the fixed point property.
【英文摘要】
We get the characterizations of the family of all nonnegative,subadditive,β-absolutely homogeneous and continuous functionals defined on X,when the β-normed space X contains an asymptotically isometric copy of lβ.Moreover,it is proved that if a closed bounded β-convex subset K of a β-normed space contains an asymptotically isometric lβ-basis,then K contains a closed β-convex subset C which fails the fixed point property.
【基金】
Supported by the Science and Technology Foundation of Educational Committee of Tianjin (Grant No.20060402)
【更新日期】
2010-12-03
【分类号】
O177.3
【正文快照】
1) x ≥ 0 and x = 0 if and only if x = θ;2) x + y ≤ x + y , for all x,y ∈ X;3) λx = |λ|β x , for all x ∈ X,λ ∈ R.It is easy to note that β-normed spaces are locally β-convex.Definition 1.3 ([5]) Let X be a vector space and A be a subset of X. I
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