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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The author wishes to thank the referee for all his/her remarks and suggestions.
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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
Key words and phrases
- invertibility
- absolute value
- normal
- self-adjoint and positive operators
- Cartesian decomposition
- bounded and unbounded operators