Essential spectra in non-Archimedean fields

  • A. Ammar Department of Mathematics, University of Sfax Lviv Politechnic National University Faculty of Sciences of Sfax Sfax, Tunisia
  • F. Z. Boutaf Department of Mathematics, University of Sfax Lviv Politechnic National University Faculty of Sciences of Sfax Sfax, Tunisia
  • A. Jeribi Department of Mathematics, University of Sfax Lviv Politechnic National University Faculty of Sciences of Sfax Sfax, Tunisia
Keywords: non-Archimedean fields;, p-adic Fredholm operator;, essential spectra

Abstract

In the paper we extend some aspects of the essential spectra theory of linear operators acting in non-Archimedean (or p-adic) Banach spaces. In particular, we establish sufficient conditions for the relations between the essential spectra of the sum of two bounded linear operators and the union of their essential spectra. Moreover, we give essential prerequisites by studying the duality between p-adic upper and p-adic lower semi-Fredholm operators. We close this paper by giving some properties of the essential spectra.

Author Biographies

A. Ammar, Department of Mathematics, University of Sfax Lviv Politechnic National University Faculty of Sciences of Sfax Sfax, Tunisia

Department of Mathematics, University of Sfax
Lviv Politechnic National University
Faculty of Sciences of Sfax
Sfax, Tunisia

F. Z. Boutaf, Department of Mathematics, University of Sfax Lviv Politechnic National University Faculty of Sciences of Sfax Sfax, Tunisia

Department of Mathematics, University of Sfax
Lviv Politechnic National University
Faculty of Sciences of Sfax
Sfax, Tunisia

A. Jeribi, Department of Mathematics, University of Sfax Lviv Politechnic National University Faculty of Sciences of Sfax Sfax, Tunisia

Department of Mathematics, University of Sfax
Lviv Politechnic National University
Faculty of Sciences of Sfax
Sfax, Tunisia

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Published
2022-10-31
How to Cite
Ammar, A., Boutaf, F. Z., & Jeribi, A. (2022). Essential spectra in non-Archimedean fields. Matematychni Studii, 58(1), 82-93. https://doi.org/10.30970/ms.58.1.82-93
Section
Articles