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.

中文翻译：

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关于算子和的可逆性

本文的主要目的是研究有界和无界设置中算子和的可逆性问题。给出了一些有趣的例子和后果。作为说明点，我们刻画了正规算子类的可逆性。此外，我们给出了具有实谱的正规算子的自伴随性的非常简短的证明。