On the Point Spectrum of Self-Adjoint Operators That Appears under Singular Perturbations of Finite Rank
We discuss purely singular finite-rank perturbations of a self-adjoint operator A in a Hilbert space ℋ. The perturbed operators \(A\) are defined by the Krein resolvent formula \((A - z)^ - 1 = (A - z)^ - 1 + B_z \) , Im z ≠ 0, where B z are finite-rank operators such that dom B z ∩ dom A = |0