Absolutely convergent extensions of nonclosable positive linear functionals (Q980476)

Let \(A\) be a topological {*}-algebra with a continuous involution and let \(A_0\) be a dense {*}-subalgebra. The authors consider the question when a (not necessarily continuous or not even closable) positive linear functional \(\omega\) on \(A_0\) can be extended to a larger subalgebra or subspace of \(A\). They obtain some sufficient conditions in this direction.