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 $…
Perturbations not necessarily commutative
Zakariae Aznay, Abdelmalek Ouahab, Hassan Zariouh
This paper treatises the preservation of some spectra under perturbations not necessarily commutative and generalizes several results which have been proved in the case of commutin…
Generalization of some commutative perturbation results
Zakariae Aznay, Abdelmalek Ouahab, Hassan Zariouh
We study the stability of certain spectra under some algebraic conditions weaker than the commutativity and we generalize many known commutative perturbation results.
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…
Generalization of Kato's decomposition
Zakariae Aznay, Abdelmalek Ouahab, Hassan Zariouh
The Kato's decomposition \cite[Theorem 4]{kato} is generalized to semi-B-Fredholm operators.
On the index of pseudo B-Fredholm operator
Zakariae Aznay, Abdelmalek Ouahab, Hassan Zariouh
The index of a pseudo B-Fredholm operator will be defined and generalize the usual index of a B-Fredholm operator. This concept will be used to extend some known results in Fredhol…
On subclasses of Browder and Weyl operators
Zakariae Aznay, Abdelmalek Ouahab, Hassan Zariouh
The main purpose of this paper, is to introduce and study the classes and which are strongly related to what has been recently studied in \cite{aznay-zariouh}…