Singularly perturbed normal operators
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.
KeywordsNormal Operator Singular Perturbation Separable Hilbert Space Singularly Perturb Normal Extension
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