DJABRI, Kenza2020-10-212020-10-212020http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/20012In this work, we discussed the spectrum continuity of some parts of the essential spectrum using a specific mode of convergence. more precisely, we investigate the relation between the essential approximate point spectrum of a sequence of bounded linear operators (𝑇𝑛)𝑛∈ℕ on Banach space 𝑋 and the essential approximate point spectrum of a linear operator 𝑇 on X, where (𝑇𝑛)𝑛∈ℕ convergent to T in 𝑣-convergence sense.enEssential spectrum, the 𝑣-convergence, spectral continuity.Thesis