Isomorphisms Between the Multiplier Algebras of Certain Topological Algebras

We study the topological algebra identification of the multiplier algebra of a certain algebra E and that of a closed left ideal in E. The case when one of the algebras is a Segal topological algebra in the other is considered. We also study this problem in the context of locally \(C^{*}\) $C^{\ast }$ -algebras.