J-Class Weighted Shifts on the Space of Bounded Sequences of Complex Numbers

We provide a characterization of J-class and Jmix-class unilateral weighted shifts on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l^{\infty} ({\mathbb{N}})$$\end{document} in terms of their weight sequences. In contrast to the previously mentioned result we show that a bilateral weighted shift on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l^{\infty} ({\mathbb{Z}})$$\end{document} cannot be a J-class operator.