Abstract
The following variant of Rellich's theorem is proved. Let A,B be operators in a Hilbert space, A=A*, BℒB* and D(B)⊃D(A). We assume that (Bu,u)⩾γ(Au,u), ∀uεD(A) for someγ> −1. Then the operator A + B with domain of definition D(A) is self-adjoint.
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Literature cited
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 147, pp. 196–198, 1985.
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Yakubov, S.Y. Perturbation of a self-adjoint operator by a subordinate symmetric operator. J Math Sci 37, 914–915 (1987). https://doi.org/10.1007/BF01387734
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DOI: https://doi.org/10.1007/BF01387734