Further results on the (b, c)-inverse, the outer inverse AT,S(2) and the Moore–Penrose inverse in the Banach context
Enrico Boasso · Linear and Multilinear Algebra · 2018
In this article, the properties of the (b, c)-inverse, the inverse along an element, the outer inverse with prescribed range and null space AT,S(2) and the Moore–Penrose inverse will be studied in the contexts of Banach spaces operators, Banach algebras and C∗-algebras. The main properties to be considered are the continuity and the differentiability. In addition, the set of all (b, c)-invertible elements will be proved to be open. The relationship between the (b, c)-inverse and the outer inverse AT,S(2) will be also characterized.