LAUSR

In this article, we study the essential pseudospectra with the class of polynomially compact operators, which is a generalization of the class of compact operators. We present some new results in essential pseudospectra for closed linear operators in Banach space with polynomially compact operators. Furthermore, we apply the obtained results to discuss the incidence of some perturbation results on left(resp. right) Weyl essential pseudospectra and left(resp. right) Fredholm essential pseudospectra. This paper aims to describe the essential pseudospectra of a sum of two bounded linear operators. As a final step, we can use the results obtained to determine the pseudo-left (right)-Fredholm spectra of 2 ? 2 block operators matrices by measuring polynomially compact operators.