发表机构
University of Tartu（塔尔图大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文勘误了凸DLD2P从M-理想提升的命题，指出量词错误，给出替代结论，并构造反例证明原声称不成立。
AI 中文摘要
在我们论文 [J. Langemets 和 K. Pirk, 直径直径二性质的稳定性, RACSAM (2021)] 的命题3.5中，我们声称凸DLD2P从$M$-理想提升到其超空间。证明中存在一个量词错误。我们证明其有效部分产生如下替代：对于每个$\varepsilon>0$，超空间单位球的每个切片包含一个$(2-\varepsilon)$ $\Delta$-点，其范数任意接近1。特别地，单位球是这些点在每个固定尺度下的闭凸包，且超空间具有局部直径二性质。最后，我们证明原始声称是错误的，我们构造了Banach空间$Y$和$X$，使得$Y$具有凸DLD2P，$Y$是$X$中的$M$-理想，但$X$不满足凸DLD2P。
英文摘要
In Proposition 3.5 of our paper [J. Langemets and K. Pirk, Stability of diametral diameter two properties, RACSAM (2021)], we claimed that the convex DLD2P lifts from an $M$-ideal to its superspace. The proof contains a quantifier error. We show that its valid part yields the following replacement: for every $\varepsilon>0$, every slice of the unit ball of the superspace contains a $(2-\varepsilon)$ $Δ$-point of norm arbitrarily close to one. In particular, the unit ball is the closed convex hull of these points at each fixed scale, and the superspace has the local diameter two property. Finally, we prove that the original claim was false, we construct Banach spaces $Y$ and $X$ such that $Y$ has the convex DLD2P, $Y$ is an $M$-ideal in $X$, yet $X$ fails the convex DLD2P.
