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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Banach-Mazur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. |
| 关键词: 仿射不变距离 凸体 Banach-Mazur距离 极体 |
| DOI： |
| 分类号:O184;O177.99 |
| 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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| THE EQUIVALENCE AND ESTIMATE OF SEVERAL AFFINE INVARIANT DISTANCES BETWEEN CONVEX BODIES |
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SHAO Yong-chong,GUO Qi
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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. |
| Key words: affine invariant distance convex body Banach-Mazur distance polar set |
