Abstract

The generalised Fredholm operators of Caradus are extended to the context of a unital homomorphism TA→B of Banach algebras. In this note we define generalised T-Fredholm element in A as the set of all elements a∈A such that T (a) is relatively regular in B and for some generalised inverse b ∈B holds e –T(a)b -bT (a) B^-1.