Extension of C*-algebras and Moore-Penrose stability of sequences of additive operators Original Research Article

An extension image of a C*-algebraimage by some element m, which has a number of special properties is proposed. These properties allow us to introduce some suitable operations of addition, multiplication and involution on image after which we are able to study different kinds of Moore-Penrose invertibility in image. Due to such an approach, we obtain necessary and sufficient conditions of weak asymptotic Moore-Penrose invertibility for an algebra arising from spline approximation methods for singular integral equations with conjugation.