Generalized inverses and the maximal radius of regularity of a Fredholm   operator
  Operators possessing analytic generalized inverses satisfying the resolvent identity are studied. Several characterizations and necessary conditions are obtained. The maximal radius of regularity for a Fredholm operator T is computed in terms of the spectral radius of a generalized inverse of T. This provides a partial answer to a conjecture of J. Zem\'anek. 
Catalin Badea and Mostafa Mbekhta