Pseudospectra in a non-Archimedean Banach space and essential pseudospectra in Eω

Abstract

In this work, we introduce and study the pseudospectra and the essential pseudospectra of linear operators respectively in the non-Archimedean Banach space and in the non-Archimedean Hilbert space Eω. In particular, we characterize these pseudospectra. Furthermore, inspired by T. Diagana and F. Ramaroson [12], we establish a relationship between the essential pseudospectrum of a closed operator and the essential pseudospectrum of this closed operator perturbed by completely continuous operator in the non-Archimedean Hilbert space Eω.