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
Full Text:

References:

 [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 [4] DOI: 10.1080/03081087408817070 [5] DOI: 10.2307/2695474 · Zbl 0993.47009 [6] DOI: 10.1016/S0024-3795(01)00297-X · Zbl 0988.15002 [7] DOI: 10.1016/S0024-3795(98)10017-4 · Zbl 0937.15002 [8] DOI: 10.1090/S0002-9939-99-05267-3 · Zbl 0935.46014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.