ON ISOMETRIC REPRESENTATION SUBSETS OF BANACH SPACES
ON ISOMETRIC REPRESENTATION SUBSETS OF BANACH SPACES
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DOI：
10.1017/s0004972715001422
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发表时间：
2015-12
影响因子：
0.7
通讯作者：
Yu Zhou;Zihou Zhang;Chunyan Liu
中科院分区：
文献类型：
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作者：
Yu Zhou;Zihou Zhang;Chunyan Liu
设X，Y是两个Banach空间，B X是X的闭单位球.我们证明了如果存在等距$f：B_{X}\rightarrow Y$且$f（0）=0$，则存在等距$F：X\rightarrow Y^{\ast \ast }$.此外，如果$Y$是弱近严格凸的，则存在等距$F：X\rightarrow Y$。利用这些结果，我们证明了：如果Y是弱近严格凸的，且存在等距函数f：B_{X}\rightarrow Y，且f（0）=0，则存在线性等距函数S：X\rightarrow Y.
Let $X,Y$ be two Banach spaces and $B_{X}$ the closed unit ball of $X$. We prove that if there is an isometry $f:B_{X}\rightarrow Y$ with $f(0)=0$, then there exists an isometry $F:X\rightarrow Y^{\ast \ast }$. If, in addition, $Y$ is weakly nearly strictly convex, then there is an isometry $F:X\rightarrow Y$. Making use of these results, we show that if $Y$ is weakly nearly strictly convex and there is an isometry $f:B_{X}\rightarrow Y$ with $f(0)=0$, then there exists a linear isometry $S:X\rightarrow Y$.