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arXiv · 1804.07288

On the Invertibility of the Sum of Operators

Mohammed Hichem Mortad
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Abstract

The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. 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 when the latter has a real spectrum.

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Mohammed Hichem Mortad. 2018-04-19. On the Invertibility of the Sum of Operators. https://arxiv.org/abs/1804.07288

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