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ЖУРНАЛЫ // Eurasian Mathematical Journal // Архив

Eurasian Math. J., 2023, том 14, номер 2, страницы 79–93 (Mi emj471)

$n$-Multiplicity and spectral properties for $(M, k)$-quasi-$*$-class $Q$ operators

A. Nasli Bakira, S. Mecherib

a Department of Mathematics, Hassiba Benbouali University of Chlef, B.P. 78C, Ouled Fares, 02180 Chlef, Algeria
b Department of Mathematics, Faculty of Science and Informatics, El Bachir Ibrahimi University, Bordj Bou Arreridj, Algeria

Аннотация: In the present article, we introduce a new class of operators which will be called the class of $(M, k)$-quasi-$*$-class $Q$ operators. An operator $A\in B(H)$ is said to be $(M, k)$-quasi-$*$-class $Q$ for certain integer $k$, if there exists $M>0$ such that
$$ A^{*k}(MA^{*2}A^2-2AA^*+I)A^k\geqslant0. $$
Some properties of this class of operators are shown. It is proved that the considered class contains the class of $k$-quasi-$*$-class $\mathbb{A}$ operators. The decomposition of such operators, their restrictions on invariant subspaces, the $n$-multicyclicity and some spectral properties are also presented. We also show that if $\lambda\in\mathbb{C}$, $\lambda\ne0$ is an isolated point of the spectrum of $A$, then the Riesz idempotent $E$ for $\lambda$ is self-adjoint, and verifies $EH=ker(A-\lambda)=ker(A-\lambda)^*$.

Ключевые слова и фразы: hyponormal operators, $(M, k)$-quasi-$*$-class $Q$ operators, $k$-quasi-$*$-class $\mathbb{A}$ operators.

MSC: 47A30, 47B47, 47B20

Поступила в редакцию: 17.06.2021

Язык публикации: английский

DOI: 10.32523/2077-9879-2023-14-2-79-93



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