Perturbation of the self-adjoint operator by the subordinated symmetric operator.

The following variant of the Rellich's theorem is proved. Let $A$, $B$ be the operators in some Hilbert space, $A=A^\ast$, $B\subset B^\ast$ and $D(B)\supset D(A)$. Let us suppose that, with some $\gamma>-1$, $(Bu,u)\geq\gamma(Au,u)$, $\forall u\in D(A)$. Then the operator $A+B$ is self-adjoint on the domain $D(A)$.