On the Gel'fand Theory for Topological Algebras

We present conditions under which the Gel'fand transform E perpendicular to,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E<^>{\wedge },$$\end{document} of locally m-convex algebra E, is a dense subalgebra of Cc(M(E))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal {C}_{c}(\mathfrak M(E))$$\end{document}. The partition of unity and the local theorem are given for a commutative unital locally m-convex algebra.