Singularly perturbed normal operators
We present a generalization of definition'of-singularly perturbed operators to the case of normal operators. To do this, we use an idea of normal expansions of a prenormal operator and prove the relation for resolvents of normal expansions similar to the M. Krein relation for resolvents of self-adjoint expansions. In addition, we establish one-to-one correspondence between the set of singular perturbations of rank one and the set of perturbed (of rank one) operators.
English version (Springer): Ukrainian Mathematical Journal 51 (1999), no. 8, pp 1177-1187.
Citation Example: Dudkin M. Ye. Singularly perturbed normal operators // Ukr. Mat. Zh. - 1999. - 51, № 8. - pp. 1045–1053.