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math.SP2022
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 $…
math.SP2022
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…
math.SP2021
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…