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Singularly perturbed normal operators

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Abstract

We present a generalization of the definition of singularly perturbed operators to the case of normal operators. To do this, we use the idea of normal extensions of a prenormal operator and prove the relation for resolvents of normal extensions similar to the M. Krein relation for resolvents of self-adjoint extensions. In addition, we establish a one-to-one correspondence between the set of singular perturbations of rank one and the set of singularly perturbed (of rank one) operators.

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Authors
  1. M. E. Dudkin
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Additional information

Kiev Polytechnic Institute, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 8, pp. 1045–1053, August, 1999.

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Dudkin, M.E. Singularly perturbed normal operators. Ukr Math J 51, 1177–1187 (1999). https://doi.org/10.1007/BF02592506

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  • DOI: https://doi.org/10.1007/BF02592506

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