Perturbation of the self-adjoint operator by the subordinated symmetric operator.
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 17, Tome 147 (1985), pp. 196-198
Voir la notice de l'article provenant de la source Math-Net.Ru
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 $D(A)$.
@article{ZNSL_1985_147_a17,
author = {S. A. Yakubov},
title = {Perturbation of the self-adjoint operator by the subordinated symmetric operator.},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {196--198},
publisher = {mathdoc},
volume = {147},
year = {1985},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_147_a17/}
}
S. A. Yakubov. Perturbation of the self-adjoint operator by the subordinated symmetric operator.. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 17, Tome 147 (1985), pp. 196-198. http://geodesic.mathdoc.fr/item/ZNSL_1985_147_a17/