On nonsymmetric rank one singular perturbations of selfadjoint operators - Vdovenko, T.; Dudkin, M. E. (Methods of Functional Analysis and Topology, 2016)
We consider nonsymmetric rank one singular perturbations of a selfadjoint operator, i.e., an expression of the form A=A+α·,ω_1ω_2, ω_1 ot=ω_2, αC, in a general case ω_1,ω_2H_-2. Using a constructive description of the perturbed operator A, we investigate some spectral and approximations properties of A. The wave operators corresponding to the couple A, A and a series of examples are also presented.