Multipliers of uniform topological algebras

Let $E$ be a complete uniform topological algebra with Arens-Michael normed factors ${\left(E_{\alpha }\right)}_{\alpha \in \mathrm{\Lambda }}\mathrm{.}$ Then $M\left(E\right) \cong \varprojlim M\left(E_{\alpha}\right)$withinanalgebraisomorphism$\varphi$\mathrm{.}Ifeachfactor$E_{\alpha}$iscomplete,theneverymultiplierof$E$iscontinuousand$\varphi$isatopologicalalgebraisomorphismwhere$M\left(E\right)$ is endowed with its seminorm topology.