A slight extension of the noncommutative integral (Q2906228)

In this short paper, the author continues his previous studies on the problem of extending positive linear functionals defined on a \(^*\)-algebra \({\mathfrak A}_0\) to a larger topological \(^*\)-algebra \({\mathfrak A}\) which densely contains \({\mathfrak A}_0\). The functionals under consideration are neither continuous nor closable; so the extensions to be used are the so-called slight extensions considered by \textit{B. Bongiorno} et al. [Rocky Mt. J. Math. 40, No. 6, 1745--1777 (2010; Zbl 1215.46036)]. In the paper under review, the author studies, in particular, slight extensions of the noncommutative integral.