In this article, we investigate the essential pseudospectra through the framework of polynomially inessential operators, which extends the class of polynomially strictly singular operators and provides a broader setting for Fredholm-type perturbations. We establish new results on the behavior of the essential pseudospectrum of closed linear operators on Banach spaces under perturbations by polynomially inessential operators. Moreover, we apply these results to study the influence of such perturbations on the left (resp. right) Weyl essential pseudospectra and the left (resp. right) Fredholm essential pseudospectra. In addition, we give a description of the essential pseudospectrum of the sum of two bounded linear operators. Finally, an application is provided to characterize the pseudo left (resp. right) Fredholm spectra of 2 × 2 block operator matrices.
Mathematics Subject Classification (2010): 47A10, 47A53, 47B06, 47A11.
Received 03 December 2024; Accepted 08 October 2025
