A characterization of the essential spectrum and applications

Jeribi, Aref

Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 3, pp. 805-825.

Abstract (VO)

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}(\Omega)$$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 in terms of boundary and collision operators assuring the invariance of the essential spectrum of the streaming operator are discussed.

Riassunto

In questo articolo lo spettro essenziale di operatori lineari chiusi e densamente definiti è caratterizzato in una grande classe degli spazi, che possiedono la proprietà di Dunford-Pettis o che sono isomorfi ad uno degli spazi $L_{p}(\Omega)$$p>1$. È dato un test di verifica pratico che garantisce la sua stabilità, per gli operatori perturbati. Inoltre applichiamo i risultati ottenuti per studiare lo spettro essenziale dell'equazione unidimensionale di trasporto con gli stati di contorno generali. Per concludere, sono discusse le condizioni sufficienti in termini di contorno e di operatori di scontro che assicurano l'invarianza dello spettro essenziale dell'operatore di flusso continuo.

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