Abstract
In this paper, we give and prove a criterion for the normality of unbounded closed operators, which is a sort of a maximality result which will be called “double maximality”. As applications, we show, under some assumptions, that the sum of two symmetric operators is essentially self-adjoint; and that the sum of two unbounded normal operators is essentially normal. Some other important results are also established.
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Notes
Kosaki [8] gave explicit examples of unbounded densely defined self-adjoint positive operators \(A\) and \(B\) such that \(D(A)\cap D(B)=\{0\}\).
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I would like to thank the referee for his comments.
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This study was Partially supported by “Laboratoire d’Analyse Mathématique et Applications”.
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Mortad, M.H. A criterion for the normality of unbounded operators and applications to self-adjointness. Rend. Circ. Mat. Palermo 64, 149–156 (2015). https://doi.org/10.1007/s12215-014-0186-2
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DOI: https://doi.org/10.1007/s12215-014-0186-2