论文标题
在连续函数空间之间的Banach-Mazur距离上
On the Banach-Mazur distance between continuous function spaces with scattered boundaries
论文作者
论文摘要
我们研究了矢量值连续函数的两个子空间之间的Banach-Mazur距离对其边界散射结构的依赖性。本着戈登的结果的精神，我们表明，在Amir-Cambern定理中出现的常数$ 2 $可以被某些类别的子空间代替$ 3 $。如果一个空间之一的弱峰值点的高度大于第二个空间的封闭边界的高度，则我们表明两个功能空间的Banach-Mazur距离至少为3。接下来，我们证明，如果考虑的高度是有限的，并且显着不同，则可以改善此估计值。作为推论，即使对于$ \ Mathcal {c}（k，e）$ spaces的情况，我们即使是新的结果。
We study the dependence of the Banach-Mazur distance between two subspaces of vector-valued continuous functions on the scattered structure of their boundaries. In the spirit of a result of Gordon, we show that the constant $2$ appearing in the Amir-Cambern theorem may be replaced by $3$ for some class of subspaces. This we achieve by showing that the Banach-Mazur distance of two function spaces is at least 3, if the height of the set of weak peak points of one of the spaces is larger than the height of a closed boundary of the second space. Next we show that this estimate can be improved, if the considered heights are finite and significantly different. As a corollary, we obtain new results even for the case of $\mathcal{C}(K, E)$ spaces.
