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On the Invertibility of the Sum of Operators

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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… Click to show full 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.

Keywords: sum operators; invertibility sum

Journal Title: Analysis Mathematica
Year Published: 2018

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