9 papers
Algebraic Direct Sums and Generalized Drazin Invertibility
Zakariae Aznay, Fadil Chabbabi
Let be a bounded linear operator on a complex Banach space . We prove that the algebraic decomposition \[ X=\K(T)\oplus \Hq(T) \] forces both summands to be closed and hence…
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 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…
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…