实秩零 $C^*$-代数中到正规元的距离
算子代数
2015-02-24 v3 泛函分析
谱理论
摘要
我们针对 Hilbert 空间上给定的有界算子 ，利用 及其到可逆算子集合的距离，得到了它到正规算子集合距离的一个在阶上达到最优的估计。在一般的实秩零 -代数中，一个稍作修改的估计依然成立。
引用
@article{arxiv.1403.2021,
title = {Distance to normal elements in $C^*$-algebras of real rank zero},
author = {Ilya Kachkovskiy and Yuri Safarov},
journal= {arXiv preprint arXiv:1403.2021},
year = {2015}
}
备注
22 pages, 10 figures. The introduction has been rewritten as the referees suggested. Some other minor amendments in the text were made, J. Amer. Math. Soc. electronically published on January 8, 2015