Ukrainian Mathematical Journal

, Volume 51, Issue 8, pp 1177–1187 | Cite as

Singularly perturbed normal operators

  • M. E. Dudkin
Article

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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Copyright information

© Kluwer Academic/Plenum Publishers 2000

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  • M. E. Dudkin

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