On the Gel’fand Theory for Topological Algebras

We present conditions under which the Gel’fand transform \(E^{\wedge },\) $E^{\wedge },$ of locally m-convex algebra E, is a dense subalgebra of \( \mathcal {C}_{c}(\mathfrak M(E))\) ${\mathcal{C}}_c(\mathfrak{M}(E))$ . The partition of unity and the local theorem are given for a commutative unital locally m-convex algebra.