论文标题
关于承包分离群空间的完整计数
On the complete metrisability of spaces of contractive semigroups
论文作者
论文摘要
单位$ C_ {0} $ - 在可分离的无限尺寸希尔伯特空间上的半群，当在均匀的弱融合拓扑中查看$ \ mathbb {r} _ {+} $的紧凑子集的拓扑，众所周知，它是众所周知的。在处理收缩案件之前，[Eisner，2010]中提出了该空间完全测能力的问题。利用Borel复杂性计算和半群的自动连续性结果，我们获得了一个一般结果，这特别意味着单个/多参数合同$ C_ {0} $ - Semigroups构成了波兰空间，因此可以正向解决开放问题。
The space of unitary $C_{0}$-semigroups on separable infinite dimensional Hilbert space, when viewed under the topology of uniform weak convergence on compact subsets of $\mathbb{R}_{+}$, is known to admit various interesting residual subspaces. Before treating the contractive case, the problem of the complete metrisability of this space was raised in [Eisner, 2010]. Utilising Borel complexity computations and automatic continuity results for semigroups, we obtain a general result, which in particular implies that the one-/multiparameter contractive $C_{0}$-semigroups constitute Polish spaces and thus positively addresses the open problem.
