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Invertibility of the sum of idempotents. (English) Zbl 1014.16031

Summary: We study necessary and sufficient conditions for the invertibility of the sum \(f+g\) when \(f\) and \(g\) are idempotents in a unital ring or bounded linear operators in Hilbert or Banach spaces. We describe the relation between the invertibility of \(f+g\) and \(f-g\).

MSC:

16U60 Units, groups of units (associative rings and algebras)
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
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[1] DOI: 10.2307/2974825 · Zbl 0901.46019
[2] DOI: 10.1090/S0002-9939-99-05233-8 · Zbl 0955.46015
[3] DOI: 10.1137/S0895479897320277 · Zbl 0946.15020
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[7] DOI: 10.1016/S0024-3795(98)10017-4 · Zbl 0937.15002
[8] DOI: 10.1090/S0002-9939-99-05267-3 · Zbl 0935.46014
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