赋范空间单位球之间的1-Lipshcitz算子 |
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引用本文: | 谭冬妮.赋范空间单位球之间的1-Lipshcitz算子[J].数学学报,2010,53(5):981-988. |
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作者姓名: | 谭冬妮 |
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作者单位: | 天津理工大学理学院 天津 300384;
南开大学数学科学学院 天津 300071 |
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基金项目: | 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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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.
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关 键 词: | 1-Lipshcitz 等距 DOPP |
收稿时间: | 2009-06-25 |
修稿时间: | 2010-04-02 |
1-Lipschitz Maps Between Unit Balls of Normed Spaces |
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Institution: | Department of Mathematics, Tianjin University of Technology, Tianjin 300384, P. R. China;
School of Mathematical Sciences, Nankai University, Tianjin 300071, P. R. China |
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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.
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Keywords: | 1-Lipschitz isometry DOPP |
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