On the essential spectra of matrix operators and applications.

Damak, Mondher; Jeribi, Aref

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A characterization of the essential spectrum and applications

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In this article the essential spectrum of closed, densely defined linear operators is characterized on a large class of spaces, which possess the Dunford-Pettis property or which isomorphic to one of the spaces $L_{p} (Ω)$ $p > 1$ . A practical criterion guaranteeing its stability, for perturbed operators, is given. Further we apply the obtained results to investigate the essential spectrum of one-dimensional transport equation with general boundary conditions. Finally, sufficient conditions...

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Let X and Y be infinite dimensional Banach spaces and let L(X,Y) be the class of all (linear continuous) operators acting between X and Y. Mil'man [5] introduced the isometry spectrum I(T) of T ∈ L(X,Y) in the following way: I(T) = {α ≥ 0: ∀ ε > 0, ∃M ∈ S_∞(X), ∀x ∈ S_M, | ||T_x|| - α | < ε}}, where S_∞(X) is the set of all infinite dimensional closed subspaces of X and S...

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