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

1996/12/19 by Catalin Badea, Cătălin Badea, Badea, Catalin +2
Computer Science · Mathematics · #47A10 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #funct-an #math.FA #msc:47A10

paper · pdf · doi:10.48550/arxiv.funct-an/9612007

LaTeX, 14 pages, to appear in Integral Equations and Operator Theory

arxiv created 1996/12/19 · openalex publication_date 1996/12/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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