论文标题
在厚度的道路指数上
On Daugavet indices of thickness
论文作者
论文摘要
受到R. Whitley的厚度指数的启发，最近提名的作者最近引入了Banach空间厚度的道路指数。我们继续研究该指数的行为，还考虑了两个新版本的Daugavet厚度指数，这有助于我们解决一个开放的问题，该问题将Daugavet指数与Daugavet方程联系起来。此外，我们将通过建立尖锐的界限来改善Daugavet指数在直接总和BANACH空间中的行为的估计值。由于我们的结果，我们证明，对于每$ 0 <Δ<2 $，就存在一个Banach空间，即单位球切片的凸组合的直径恰好是$Δ$，从而从文献中解决了一个空旷的问题。最后，我们证明，伊瓦科诺（Ivakhno）在2006年提出了一个关于切片半径和直径之间的关系的一个空旷的问题。
Inspired by R. Whitley's thickness index the last named author recently introduced the Daugavet index of thickness of Banach spaces. We continue the investigation of the behavior of this index and also consider two new versions of the Daugavet index of thickness, which helps us solve an open problem which connect the Daugavet indices with the Daugavet equation. Moreover, we will improve the formerly known estimates of the behavior of Daugavet index on direct sums of Banach spaces by establishing sharp bounds. As a consequence of our results we prove that, for every $0<δ<2$, there exists a Banach space where the infimum of the diameter of convex combinations of slices of the unit ball is exactly $δ$, solving an open question from the literature. Finally, we prove that an open question posed by Ivakhno in 2006 about the relation between the radius and diameter of slices has a negative answer.
