| 凸体间几种仿射不变距离的等价性与估计 |
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| 引用本文： | 邵永冲,国起. 凸体间几种仿射不变距离的等价性与估计[J]. 数学杂志, 2015, 35(2): 287-293 |
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| 作者姓名： | 邵永冲 国起 |
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| 作者单位： | 苏州科技学院数学系 |
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| 基金项目： | Supported partially by National Natural Science Foundation of China(11271282);partially by the GIF of Jiangsu(CXLX11_0960) |
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| 摘 要： | 本文研究了凸体间(绝对)Banach-Mazur距离各种不同的定义,证明了它们的等价性;给出了Banach-Mazur距离与绝对Banach-Mazur距离相等的一个充分条件;最后研究了凸体极体间的BanachMazur距离,并对特殊凸体对证明了其Banach-Mazur距离与其某一对极体间的Banach-Mazur距离相等.文中结果为Banach-Mazur距离最佳上界的估计提供了进一步研究的基础.
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| 关 键 词： | 仿射不变距离 凸体 Banach-Mazur距离 极体 |
| 收稿时间： | 2012-10-30 |
| 修稿时间： | 2013-04-11 |
THE EQUIVALENCE AND ESTIMATE OF SEVERAL AFFINE INVARIANT DISTANCES BETWEEN CONVEX BODIES |
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| SHAO Yong-chong and GUO Qi. THE EQUIVALENCE AND ESTIMATE OF SEVERAL AFFINE INVARIANT DISTANCES BETWEEN CONVEX BODIES[J]. Journal of Mathematics, 2015, 35(2): 287-293 |
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| Authors: | SHAO Yong-chong and GUO Qi |
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| Affiliation: | SHAO Yong-chong;GUO Qi;Department of Mathematics,Suzhou University of Science and Technology; |
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| Abstract: | In this paper, the equivalences of several different definitions of two types of Banach-Mazur distance between convex bodies are shown respectively, the conditions under which these two types of Banach-Mazur distance coincide are discussed, and the Banach-Mazur distances between polar bodies of special convex bodies are studied as well. The results obtained here will play some role in estimating the best upper bound of Banach-Mazur distances. |
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| Keywords: | affine invariant distance convex body Banach-Mazur distance polar set |
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