Author:
Ammar A.,Boutaf F. Z.,Jeribi A.
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.
Publisher
Ivan Franko National University of Lviv
Reference18 articles.
1. F. Abdmouleh, A. Jeribi, Gustafson, Weidman, Kato, Wolf, Schechter, Browder, Rakocevic and Schmoeger essential spectra of the sum of two bounded operators and application to a transport operator, Math. Nachr., 284 (2011), №2-3, 166–176.
2. J. Araujo, C. Perez-Garcia, S. Vega, Preservation of the index of p-adic linear operators under compact perturbations, Compositio Math., 118 (1999), №3, 291–303.
3. T. Diagana, Non-Archimedean linear operators and applications, Nova Science Publishers, Inc., Huntington, NY, xiv+92 pp. ISBN: 978-1-60021-405-9; 1-60021-405-3, 2007.
4. T. Diagana, F. Ramaroson, Non-Archimedean operator theory. SpringerBriefs in Mathematics. Springer, Cham, 2016.
5. T. Diagana, R. Kerby, TeyLama H. Miabey, F. Ramaroson, Spectral analysis for finite rank perturbations of diagonal operators in non-archimedean Hilbert space, P-Adic Num. Ultrametr. Anal. Appl., 6 (2014), №3, 171–187. https://doi.org/10.1134/S2070046614030017