Iranian Mathematical Society Journal of the Iranian Mathematical Society 2717-1612 5 2 2024 03 01 Characterization of the structured pseudospectrum in non-Archimedean Banach spaces 79 93 194146 10.30504/jims.2024.446376.1163 EN J. Ettayb Department of Mathematics, Sidi Mohamed Ben Abdellah University, Fez, Morocco. Journal Article 2024 03 01 In this paper, we demonstrate some results on the pseudospectrum of linear operator pencils on non-Archimedean Banach spaces. In particular, we give a relationship between the Fredholm spectrum of a bounded operator pencil $(A,B)$ and the Fredholm spectrum of the pencil $(A^{-1},B^{-1}).$ Also, we establish a characterization of the essential spectrum of operator pencils on non-Archimedean Banach spaces. Furthermore, we introduce and study the structured pseudospectrum of linear operators on non-Archimedean Banach spaces. We prove that the structured pseudospectra associated with various $\varepsilon$ are nested sets and the intersection of all the structured pseudospectra is the spectrum. We establish a characterization of the structured pseudospectrum of bounded linear operators on non-Archimedean Banach spaces. Finally, we characterize the structured essential pseudospectrum of bounded linear operator pencils on non-Archimedean Banach spaces and we give an illustrative example. https://jims.ims.ir/article_194146_09fa647f2fd39990684a6e3f431f80f8.pdf