Local version of approximation theorem and of λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document}-tensor product of operator systems

Local operator systems are projective limits of operator systems. In this paper, we discuss several tensor products including minimal (lmin), maximal (lmax), local commuting, and λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document}-tensor product in the category of local operator systems. A characterization of (lmin, lmax)-nuclearity is given which is local version of approximation theorem. We also show that projective limit of operator systems having completely positive factorization property (CPFP) is a local operator system having local completely positive factorization property (LCPFP).