论文标题
收缩$ C_ {0} $ - Semigroups是Baire空间
The space of contractive $C_{0}$-semigroups is a Baire space
论文作者
论文摘要
在无限的尺寸可分离的希尔伯特空间上工作，在均匀的弱操作员收敛下，在$ \ mathbb {r} _ {+} $的紧凑子集对紧凑型子集的拓扑拓扑中取得了剩余的结果。 Eisner和Serény在2009年提出了一个空旷的问题：这个空间构成了Baire空间吗？观察到统一半群的子空间是完全可以进行的，并且对已知密度结果有吸引力，我们通过证明某些拓扑特性通常可以从密集的子空间转移到较大的空间来积极解决此问题。转移结果反过来依赖于通过无限游戏对拓扑特性的分类。我们的方法足够一般，可以应用于其他情况，例如PW-Topology下的收缩空间。
Working over infinite dimensional separable Hilbert spaces, residual results have been achieved for the space of contractive $C_{0}$-semigroups under the topology of uniform weak operator convergence on compact subsets of $\mathbb{R}_{+}$. Eisner and Serény raised in 2009 the open problem: Does this space constitute a Baire space? Observing that the subspace of unitary semigroups is completely metrisable and appealing to known density results, we solve this problem positively by showing that certain topological properties can in general be transferred from dense subspaces to larger spaces. The transfer result in turn relies upon classification of topological properties via infinite games. Our approach is sufficiently general and can be applied to other contexts, e.g. the space of contractions under the pw-topology.
