Spectral analysis for a class of bounded linear operators

TL;DR

This paper investigates the spectral properties of a specific class of bounded linear operators on non-Archimedean Hilbert spaces, utilizing Fredholm theory to derive key results.

Contribution

It introduces a spectral analysis framework for operators composed of diagonal and finite-rank parts in non-Archimedean Hilbert spaces, leveraging Fredholm operator theory.

Findings

Characterization of the spectrum for the operator class

Application of Fredholm theory to spectral analysis

Results on the structure of spectra in non-Archimedean settings

Abstract

We study the Spectral Analysis for a class of bounded linear operators T = D + F in a non Archimedean Hilbert space E, where D is a diagonal linear operator and where F is a finite rank linear operator. In this study of the Spectral Analysis, we use extensively the Theory of Fredholm Operators to deduce some of our main results.