关于压缩半群空间的完全可度量化
泛函分析
2023-02-02 v4
摘要
在可分离无限维Hilbert空间上的酉-半群空间,在紧子集上一致弱收敛拓扑下考察时,已知具有若干有趣的剩余子空间。在处理压缩情形之前,[Eisner, 2010]中提出了该空间的完全可度量化问题。利用Borel复杂度计算与半群的自动连续性结果,我们得到一个一般结果,其特别地蕴含单参数/多参数压缩-半群构成Polish空间,从而正面解决了该开放问题。
引用
@article{arxiv.2010.01573,
title = {On the complete metrisability of spaces of contractive semigroups},
author = {Raj Dahya},
journal= {arXiv preprint arXiv:2010.01573},
year = {2023}
}
备注
Minor stylistic changes. Appendix included which provides a larger class of examples to which the main result applies. Note that this appendex consists of the content of the author's paper 'On the strong continuity of generalised semigroups' (arXiv:2009.04393)