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Eurasian Mathematical Journal, 2017, том 8, номер 1, страницы 119–127
(Mi emj251)
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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Unconditional bases of subspaces related to non-self-adjoint perturbations of self-adjoint operators
A. K. Motovilovab, A. A. Shkalikovc a Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 6 Joliot-Curie St, 141980 Dubna, Moscow Region, Russia
b Faculty of Natural and Engineering Sciences, Dubna State University,
19 Universitetskaya St, 141980 Dubna, Moscow Region, Russia
c Faculty of Mathematics and Mechanics, M.V. Lomonosov Moscow State University, 1 Leninskiye Gory St, 119991 Moscow GSP-1, Russia
Аннотация:
Assume that $T$ is a self-adjoint operator on a Hilbert space $\mathcal{H}$ and that the spectrum of $T$ is contained in the union $\bigcup_{j\in J}\Delta_j$, $J\subseteq\mathbb{Z}$, of the segments $\Delta_j = [\alpha_j,\beta_j]\subset \mathbb{R}$ such that
$\alpha_{j+1}>\beta_j$ and
$$
\inf_j(\alpha_{j+1}-\beta_j)=d>0.
$$
If $B$ is a bounded (in general non-self-adjoint) perturbation of $T$ with $||B||=:b<d/2$, then the
spectrum of the perturbed operator $A=T+B$ lies in the union $\bigcup_{j\in J}U_b(\Delta_j)$ of the mutually
disjoint closed $b$-neighborhoods $U_b(\Delta_j)$ of the segments $\Delta_j$ in $\mathbb{C}$. Let $Q_j$ be the Riesz projection
onto the invariant subspace of $A$ corresponding to the part of the spectrum of $A$ lying in $U_b(\Delta_j)$, $j\in J$. Our main result is as follows: The subspaces $\mathcal{L}_j=Q_j(\mathcal{H})$, $j \in J$ form an unconditional
basis in the whole space $\mathcal{H}$.
Ключевые слова и фразы:
Riesz basis, unconditional basis of subspaces, non-self-adjoint perturbations.
Поступила в редакцию: 23.01.2017
Образец цитирования:
A. K. Motovilov, A. A. Shkalikov, “Unconditional bases of subspaces related to non-self-adjoint perturbations of self-adjoint operators”, Eurasian Math. J., 8:1 (2017), 119–127
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj251 https://www.mathnet.ru/rus/emj/v8/i1/p119
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Страница аннотации: | 354 | PDF полного текста: | 117 | Список литературы: | 42 |
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