Generalized inverses and the maximal radius of regularity of a Fredholm operator

Abstract

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. Zemánek.

arXiv commentLaTeX, 14 pages, to appear in Integral Equations and Operator Theory