Commutative Algebras of Toeplitz Operators on the Reinhardt Domains

Let D be a bounded logarithmically convex complete Reinhardt domain in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\mathbb{C}}^n$$ \end{document} centered at the origin. Generalizing a result for the one-dimensional case of the unit disk, we prove that the C*-algebra generated by Toeplitz operators with bounded measurable separately radial symbols (i.e., symbols depending only on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$|z_1|, |z_2|, \ldots , |z_n|)$$ \end{document} is commutative.