Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 17, Tome 147 (1985), pp. 196-198
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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/
@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},
year = {1985},
volume = {147},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_147_a17/}
}
TY - JOUR
AU - S. A. Yakubov
TI - Perturbation of the self-adjoint operator by the subordinated symmetric operator.
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1985
SP - 196
EP - 198
VL - 147
UR - http://geodesic.mathdoc.fr/item/ZNSL_1985_147_a17/
LA - ru
ID - ZNSL_1985_147_a17
ER -
%0 Journal Article
%A S. A. Yakubov
%T Perturbation of the self-adjoint operator by the subordinated symmetric operator.
%J Zapiski Nauchnykh Seminarov POMI
%D 1985
%P 196-198
%V 147
%U http://geodesic.mathdoc.fr/item/ZNSL_1985_147_a17/
%G ru
%F ZNSL_1985_147_a17
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 $D(A)$.
