ON A CHARACTERIZATION OF THE S-ESSENTIAL SPECTRA OF THE SUM AND THE PRODUCT OF TWO OPERATORS AND APPLICATION TO A TRANSPORT OPERATOR

摘要

In this paper,we develop some operational calculus inspired from the Fredholm operator theory to investigate the S-essential spectra of the sum and the product of two operators acting on a Banach space.Furthermore,we apply the obtained results to determine the S-essential spectra of an integro-differential operator with abstract boundary conditions in L_1([-α,α]×[-1,1])(α > 0).