2015/03/23 by Hassan Zariouh, H. Zariouh, Hassane Zguitti +3
Mathematics · #47A10 #47A11 #47A53 #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #math.FA #msc:47A10 #msc:47A11 #msc:47A53
paper · pdf · doi:10.48550/arxiv.1503.06611
arxiv created 2015/03/23 · openalex publication_date 2015/03/23 · arxiv updated 2015/03/24 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We introduce a new class which generalizes the class of B-Weyl operators. We say that T∈ L(X) is pseudo B-Weyl if T=T1⊕ T2 where T1 is a Weyl operator and T2 is a quasi-nilpotent operator. We show that the corresponding pseudo B-Weyl spectrum σpBW(T) satisfies the equality σpBW(T)∪[\mathcal S(T)∩\mathcal S(T^*)]=σgD(T); where σgD(T) is the generalized Drazin spectrum of T∈ L(X) and \mathcal S(T) (resp., \mathcal S (T^*)) is the set where T (resp., T^*) fails to have SVEP. We also investigate the generalized Drazin invertibility of upper triangular operator matrices by giving sufficient conditions which assure that the generalized Drazin spectrum or the pseudo B-Weyl spectrum of an upper triangular operator matrices is the union of its diagonal entries spectra.