Resumen de Spectral properties for polynomial and matrix operators involving demicompactness classes

Fatma Ben Brahim

• The first aim of this paper is to show that a polynomially demicompact operator satisfying certain conditions is demicompact. Furthermore, we give a refinement of the Schmo¨eger and the Rakocevi´c essential spectra of a closed linear operator involving the class of demicompact ones. The second aim of this work is devoted to provide some sufficient conditions on the inputs of a closable block operator matrix to ensure the demicompactness of its closure. An example involving the Caputo derivative of fractional of order α is provided.

  Moreover, a study of the essential spectra and an investigation of some perturbation results