%0 Journal Article
%T 凸体间几种仿射不变距离的等价性与估计<br>THE EQUIVALENCE AND ESTIMATE OF SEVERAL AFFINE INVARIANT DISTANCES BETWEEN CONVEX BODIES
%A 作者
%A 邵永冲
%A 国起
%J 数学杂志
%D 2015
%X 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.<br>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
%K 仿射不变距离 凸体 Banach-Mazur距离 极体&lt
%K br&gt
%K affine invariant distance convex body Banach-Mazur distance polar set
%U http://sxzz.whu.edu.cn/sxzz/ch/reader/view_abstract.aspx?file_no=20150208&flag=1