Graph C*-Algebras and Their Ideals Defined by Cuntz-Krieger Family of Possibly Row-Infinite Directed Graphs

Let E be a possibly row-infinite directed graph. In this paper, first we prove the existence of the universal C*-algebra C*(E) of E which is generated by a Cuntz-Krieger E-family {se, pv}, and the gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem for the ideal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{K}_E $$\end{document} of C*(E). Then we get our main results about the ideal structure of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{K}_E .$$\end{document} Finally the simplicity and the pure infiniteness of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{K}_E .$$\end{document} is discussed.