Characterization of the structured pseudospectrum in non-Archimedean Banach spaces

Articles in Press

Document Type : Research Article

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Department of Mathematics, Faculty of Sciences Dhar El Mehrez, Fès, Morocco

Abstract

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.

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Journal of the Iranian Mathematical Society

Articles in Press, Accepted Manuscript
Available Online from 15 April 2024

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