Representable linear functionals on partial \(*\)-algebras (Q414396)

The paper deals with \(*\)-representations of topological \(*\)-algebras. First, it is shown that a Gelfand-Naimark-Segal-like construction is possible for representable linear functionals. Then invariant positive sesquilinear forms are studied. As a main result, it is shown that for a positive sesquilinear form \(\phi\) for which a pre-core \(B(\phi)\) exists, there exists an invariant positive sesquilinear form \(\phi_0\) for which \(B(\phi)\) is a core and for which \(\phi\) coincides with \(\phi_0\) in quite a large region. In the last part, regular and quasi regular \(*\)-representations of a partial \(*\)-algebra are studied.