Extension of \(C^*\)-algebras and Moore-Penrose stability of sequences of additive operators (Q1307198)

The paper deals with an extension \(\widetilde{\mathcal A}\) of a \(C^*\)-algebra \({\mathcal A}\) by some element \(m\). The authors introduce suitable operations of addition, multiplication and involution on \(\widetilde{\mathcal A}\) and then study different kinds of Moore-Penrose invertibility in \(\widetilde{\mathcal A}\). Necessary and sufficient conditions of the weak asymptotic Moore-Penrose invertibility are obtained for a wide class of numerical methods based on splines of prescribed degree.