Absolutely Convergent Extensions of Nonclosable Positive Linear Functionals

The existence of extensions of a positive linear functional ω defined on a dense *-subalgebra \mathfrakA₀{\mathfrak{A}_0} of a topological *-algebra \mathfrakA{\mathfrak{A}}, satisfying certain regularity conditions, is examined. The main interest is focused on the case where ω is nonclosable and sufficient conditions for the existence of an absolutely convergent extension of ω are given.