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7 papers
Almost invertible operators
Zakariae Aznay, Abdelmalek Ouahab, Hassan Zariouh
We prove that a bounded linear operator is a direct sum of an invertible operator and an operator with at most countable spectrum iff $0\notin\mbox{acc}^{ω_{1}}\,σ(T),$ where $…
On the -Kato decomposition and generalization of Koliha Drazin invertibility
Z. Aznay, A. Ouahab, H. Zariouh
In \cite{koliha}, Koliha proved that ( is a complex Banach space) is generalized Drazin invertible operator equivalent to there exists an operator commuting with…
On the class -operators
Zakariae Aznay, Hassan Zariouh
It is well known that an hyponormal operator satisfies Weyl's theorem. A result due to Conway shows that the essential spectrum of a normal operator consists precisely of all p…
Extended Rakočević's property
kaoutar Ben Ouidren, Hassan Zariouh
The purpose of this paper is to introduce and study new extension of Rakočević's property and property introduced by Berkani--Zariouh in \cite{berkani-zariouh1}, in con…
The Berkani's property and a note on some recent results
Zakariae Aznay, Hassan Zariouh
In this paper, we continue the study of property introduced in \cite{berkani2}, in connection with other Weyl type theorems. Moreover, we give counterexamples to show that…
Property (z); direct sums and a note on an a-Browder type theorem
A. Arroud, H. Zariouh
We characterize the properties and for an operator whose dual has the SVEP on the complementary of the upper semi-Weyl spectrum of If and are Ba…