凸体间几种仿射不变距离的等价性与估计
THE EQUIVALENCE AND ESTIMATE OF SEVERAL AFFINE INVARIANT DISTANCES BETWEEN CONVEX BODIES

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.
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