赋范空间单位球之间的1-Lipshcitz算子

谭冬妮

数学学报 ›› 2010, Vol. 53 ›› Issue (5) : 981-988.

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数学学报 ›› 2010, Vol. 53 ›› Issue (5) : 981-988. DOI: 10.12386/A2010sxxb0109
论文

赋范空间单位球之间的1-Lipshcitz算子

    谭冬妮
作者信息 +

1-Lipschitz Maps Between Unit Balls of Normed Spaces

    Dong Ni TAN
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文章历史 +

摘要

证明了赋范空间单位球之间任意保一的1-Lipshcitz算子在假设像空间是严格凸的,或者算子是满的条件下是定义在全空间上的线性等距算子在单位球上的限制.同时,也给出了这个结果的一些应用,以及当两个赋范空间是严格凸时推广了的结果.

 

Abstract

We show that every 1-Lipschitz map having DOPP between two unit balls of normed spaces is the restriction of a linear isometry on the whole space under the assumption that the map is surjective or the target space is strictly convex. We also present some applications of this result and a generalized result when both of the normed spaces are assumed to be strictly convex.

 

关键词

1-Lipshcitz / 等距 / DOPP

Key words

1-Lipschitz / isometry / DOPP

引用本文

导出引用
谭冬妮. 赋范空间单位球之间的1-Lipshcitz算子. 数学学报, 2010, 53(5): 981-988 https://doi.org/10.12386/A2010sxxb0109
Dong Ni TAN. 1-Lipschitz Maps Between Unit Balls of Normed Spaces. Acta Mathematica Sinica, Chinese Series, 2010, 53(5): 981-988 https://doi.org/10.12386/A2010sxxb0109

参考文献


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基金

国家自然科学基金资助项目(10871101);高校博士点基金资助项目

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