Spectral analysis for finite rank perturbations of diagonal operators in non-archimedean Hilbert space

Diagana, Toka; Kerby, Rodney; Miabey, TeyLama H.; Ramaroson, François

doi:10.1134/s2070046614030017

Cited by 7 publications

(2 citation statements)

References 10 publications

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“…The theory of a non-Archimedean operators, from which many valued results were obtained, has been extensively studied (see [5][6][7]9]). In recent years, a number of papers presented by diverse authors about the spectral theory of linear operators in a non-Archimedean Banach and Hilbert space have appeared such as, e.g., [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

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

Ammar

Bouchekoua

Jeribi

2019

Filomat

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In this work, we introduce and study the pseudospectra and the essential pseudospectra of linear operators in a non-Archimedean Banach space and in the non-Archimedean Hilbert space E ω , respectively. 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 linear operator and the essential pseudospectrum of this closed linear operator perturbed by completely continuous operator in the non-Archimedean Hilbert space E ω .

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Section: Introductionmentioning

confidence: 99%

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

Ammar

Bouchekoua

Jeribi

2019

Filomat

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“…However, after the reading of literature about the essential spectrum, there are not many manuscripts in the non-Archimedean setting except in [4,5], where it was defined only one type of the essential spectrum and proved that the latter is not affected by the addition of a completely continuous operator. This is our impetus to extend the other types of essential spectra in non-Archimedean fields, which we will examine in connection with various classes of linear operators defined through the kernels and ranges, the most important of these classes are p-adic Fredholm operators, p-adic upper semi-Fredholm operators, and p-adic lower semi-Fredholm operators.…”

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confidence: 99%

Essential spectra in non-Archimedean fields

Ammar¹,

Boutaf²,

Jeribi³

2022

Mat. Stud.

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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.

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Bounded Linear Operators in Non-Archimedean Banach Spaces

Diagana

Ramaroson

2016

SpringerBriefs in Mathematics

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Spectral analysis for finite rank perturbations of diagonal operators in non-archimedean Hilbert space

Cited by 7 publications

References 10 publications

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

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

Essential spectra in non-Archimedean fields

Bounded Linear Operators in Non-Archimedean Banach Spaces

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