Generalized Invertibility in Fredholm Theory
Abstract
In [5], Harte used the well-known Atkinson’s theorem (which gives a necessary and sufficient condition for a Banach space operator to be Fredholm) to introduce a Fredholm theory relative to an arbitrary Banach algebra homomorphism. In [2], Berkani defined the notion of a B-Fredholm operator - a type of generalized Fredholm operator - for which an Atkinson-type theorem was established in [3] and utilized in [4] to introduce B-Fredholm theory in general Banach algebras.



