Pseudospectrum and essential Pseudospectrum of operator pencils on ultrametric Banach spaces

Abstract

In this paper, we introduce and study the bounded linear operator pencils and pseudospectrum and essential pseudospectrum of bounded linear operator pencils on ultrametric Banach spaces. We give a characterization of the essential spectrum and essential pseudospectrum of bounded linear operator pencils $(A,B)$ where $A, B\in\mathcal{L}(E)$ by means of ultrametric Fredholm operators and we give a characterization of the essential pseudospectrum
of bounded linear operator pencils by means of the spectra of all perturbed compact operators.