Abstract

We expand the class of deviation sequences for which the problem on the existence of an element of a Banach space with these deviations from a system of nested subspaces is solved positively regardless of the space and the system of subspaces. This result is used to narrow the gap between the weak asymptotics constants in S. V. Konyagin’s theorem on the existence of an element whose deviations are asymptotically close to given ones.

中文翻译：

---

关于子空间扩展系统中给定偏差的元素的存在性

摘要

我们扩展了偏差序列的类别，对于该类，无论空间和子空间系统如何，都可以肯定地解决具有与嵌套子空间系统的这些偏差的 Banach 空间元素的存在性问题。该结果用于缩小 SV Konyagin 定理中弱渐近常数之间的差距，该定理涉及偏差渐近接近给定偏差的元素的存在性。