Search results for "invariant sesquilinear positive forms"

Extensions of Representable Positive Linear Functionals to Unitized Quasi *-Algebras: A New Method

2014

In this paper we introduce a topological approach for extending a representable linear functional \({\omega}\), defined on a topological quasi *-algebra without unit, to a representable linear functional defined on a quasi *-algebra with unit. In particular, we suppose that \({\omega}\) is continuous and the positive sesquilinear form \({\varphi_\omega}\), associated with \({\omega}\), is closable and prove that the extension \({\overline{\varphi_\omega}^e}\) of the closure \({\overline{\varphi_\omega}}\) is an i.p.s. form. By \({\overline{\varphi_\omega}^e}\) we construct the desired extension.