The singular nonsymmetric rank one perturbation of
a self-adjoint operator from classes ${\mathcal H}_{-1}$ and ${\mathcal H}_{-2}$ was considered for the first time in works by
Dudkin M.E. and Vdovenko T.I. \cite{k8,k9}. In the mentioned papers, some properties of the point spectrum are described,
which occur during such perturbations.
This paper proposes generalizations of the results presented in \cite{k8,k9} and \cite{k2} in the case of
nonsymmetric class ${\mathcal H}_{-2}$ perturbations of finite rank.
That is, the formal expression of the following is considered
\begin{equation*}
\tilde A=A+\sum \limits_{j=1}^{n}\alpha_j\langle\cdot,\omega_j\rangle\delta_j,
\end{equation*}
where $A$ is an unperturbed self-adjoint operator on a separable Hilbert space
${\mathcal H}$, $\alpha_j\in{\mathbb C}$, $\omega_j$, $\delta_j$, $j=1,2, ..., n<\infty$ are
vectors from the negative space ${\mathcal H}_{-2}$ constructed by the operator $A$,
$\langle\cdot,\cdot\rangle$ is the dual scalar product between positive and negative spaces.
Minami’s Estimate: Beyond Rank One Perturbation and Monotonicity
