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On the Invertibility of the Sum of Operators

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Abstract

The primary purpose of this paper is to investigate the question of the invertibility of the sum of operators in the bounded and unbounded setting. Some interesting examples and consequences are given. As an illustrative point, we characterize invertibility for the class of normal operators. Also, we give a very short proof of the self-adjointness of a normal operator which has a real spectrum.

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Acknowledgement

The author wishes to thank the referee for all his/her remarks and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, University of Oran 1, Ahmed Ben Bella, B.P. 1524, El Menouar, Oran, 31000, Algeria

    M. H. Mortad

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  1. M. H. Mortad
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Correspondence to M. H. Mortad.

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Mortad, M.H. On the Invertibility of the Sum of Operators. Anal Math 46, 133–145 (2020). https://doi.org/10.1007/s10476-020-0022-1

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  • DOI: https://doi.org/10.1007/s10476-020-0022-1

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