Further results on the (b, c)-inverse, the outer inverse AT,S-(2) and the Moore-Penrose inverse in the Banach context

摘要

In this article, the properties of the (b,c)-inverse, the inverse along an element, the outer inverse with prescribed range and null space A(T,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 A(T,S)((2)) will be also characterized.