Abstract
Aspects of the theory of operator ranges, factorization and range inclusion are brought to bear on some operator and approximation-theoretic problems for generalized inverses on infinite dimensional Banach and Hilbert spaces. Several criteria are given for an operator to have a bounded outer inverse with infinite rank. It is also shown using one of these criteria that the set of all bounded linear operators with a bounded outer inverse is open. The set of all bounded linear operators with a bounded inner inverse is dense in the space of all bounded linear operators. Comments on related topics in generalized inverse operator theory and some open problems are given.
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© 1981 Birkhäuser Verlag Basel
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Nashed, M.Z. (1981). On Generalized Inverses and Operator Ranges. In: Butzer, P.L., Sz.-Nagy, B., Görlich, E. (eds) Functional Analysis and Approximation. ISNM 60: International Series of Numerical Mathematics / ISNM 60: Internationale Schriftenreihe zur Numerischen Mathematik / ISNM 60: Série internationale d’Analyse numérique, vol 60. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9369-5_10
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DOI: https://doi.org/10.1007/978-3-0348-9369-5_10
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