Non-Commutative Fejér Theorems

In this paper we prove that there are operators in the uniform Roe algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C_u^*(G)}$$\end{document} which cannot be approximated by the truncations of themselves, where G is a finitely generated group. We also give a sufficient condition for the operators which can be approximated by the truncations of themselves. For a countable discrete metric space X, we obtain the similar conclusions.