Authors
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M. Berkani
Department of Mathematics, Science Faculty of Oujda, University Mohammed I, Operator Theory Team, Morocco
Author
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H. Zariouh
Centre régional des métiers de l'éducation et de la formation, B.P 458, Oujda, Morocco et Equipe de la Théorie des Opérateurs, Université Mohammed I, Faculté des Sciences d'Oujda, Dépt. de Mathématiques, Morocco
Author
Keywords:
B-Fredholm spectrum, Riesz perturbations
Subjects:
47A53, , 47A10, 47A11
Abstract
Let be a bounded linear Banach space operator and let be aquasinilpotent one commuting with . The main purpose of thepaper is to show that we do not have where , contrary to whathas been announced in the proof of Lemma 3.5 from M. Amouch,{Polaroid operators with SVEP and perturbations of property (gw)},Mediterr. J. Math. {6} (2009), 461–470, where is the Drazin spectrum of and its left Drazin spectrum. However, under the additional hypothesis, the mentioned equality holds.Moreover, we study the preservation of various spectra originatingfrom B-Fredholm theory under perturbations by Riesz operators.