On spectral continuity of the essential spectrum - DJABRI, Kenza (Faculty of Mathematics and computer sciences Department of Mathematics - Option : Mathematical and Numerical Analysis, 2020)
In 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.
Keywords: Essential spectrum, the 𝑣-convergence, spectral continuity.