论文标题
轨道的相对紧凑性和Banach空间的几何形状
Relative compactness of orbits and geometry of Banach spaces
论文作者
论文摘要
我们调查了Banach Space $ e $上的线性运算符$ S $的有界半群，当每个$ t \ in S $中的每个$ t \的相对紧凑型$ s（i-t）x $ in s $ in s $ in s $ in o $中的$ x \表示相对紧凑性的相对紧凑性。特别是，我们得出了不包含$ \ mathrm {c} _0 $的可分离Banach空间的特征，并且在这种紧凑性结果方面具有Schauder基础的Banach空间的反射性。
We investigate for a bounded semigroup of linear operators $S$ on a Banach space $E$ and a vector $x \in E$, when relative compactness of $S(I-T)x$ for every $T \in S$ implies relative compactness of the orbit $Sx$. In particular, we derive characterizations of separable Banach spaces not containing $\mathrm{c}_0$ and of reflexivity of Banach spaces with a Schauder basis in terms of such compactness results.
