Multipliers of uniform topological algebras

Abstract

Let $E$ be a complete uniform topological algebra with Arens-Michael normed factors ${\left(E_{\alpha }\right)}_{\alpha \in \Lambda }.$ Then $M\left(E\right)\cong \underleftarrow{\lim }M\left(E_{\alpha }\right)$ within an algebra isomorphism $\phi$. If each factor $E_{\alpha }$ is complete, then every multiplier of $E$ is continuous and $\phi$ is a topological algebra isomorphism where $M\left(E\right)$ is endowed with its seminorm topology.

arXiv comment8 pages