ABSTRACT
In this article, the properties of the (b, c)-inverse, the inverse along an element, the outer inverse with prescribed range and null space and the Moore–Penrose inverse will be studied in the contexts of Banach spaces operators, Banach algebras and -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 will be also characterized.
Acknowledgements
The author wishes to express his indebtedness with the referee, for her/his suggestions have improved the presentation of this article.
Notes
No potential conflict of interest was reported by the author.