arXiv subjects

Teylama Miabey

Publications and source records attributed to Teylama Miabey.

3 recordsLinked to original sources

arXiv2026

Spectral and Essential Spectral Analysis of Finite-Rank Perturbations of Unbounded Diagonal Operators on Non-Archimedean Hilbert Spaces

We study the spectral properties of a class of unbounded linear operators on a non-Archimedean Hilbert space $E_ω$. More precisely, we consider operators of the form \[ T=D+F,\qquad F=\sum_{j=1}^{m} u_j\otimes v_j, \] where $D$ is an unbounded diagonal operator and $F$ is a finite-rank perturbation. This work extends the spectral analysis of Diagana and McNeal for rank-one perturbations of diagonal operators to the case of arbitrary finite-rank perturbations. The main objective is to describe the spectrum, point spectrum, and essential spectrum of such operators in terms of the diagonal sequence associated with $D$ and the Fredholm properties of $λI-T$. The theory of Fredholm operators plays a central role, particularly in the computation of the essential spectrum and in the study of stability under finite-rank perturbations.

math.FA↗

arXiv2026

Algebraic Geometry over Non-Algebraically Closed Fields -- A-Coherent Sheaves over a Ringed Space

In this paper, we investigate the properties of $A$-coherent and $A$-quasi-coherent sheaves within the framework of algebraic geometry over non-algebraically closed fields. We define an $\mathcal{O}_X$-module to be $A$-coherent (resp. $A$-quasi-coherent) if it admits a global presentation by free modules of finite rank (resp. arbitrary rank) over a ringed space $X$. We establish a fundamental correspondence between these sheaves and modules over the ring of global sections $A = Γ(X,\mathcal{O}_X)$. Specifically, we prove that under conditions of flatness for the canonical morphism and the exactness of the global section functor, there exists an equivalence of categories between $A$-coherent $\mathcal{O}_X$-modules and finitely presented modules over $A$. We further demonstrate the utility of these results by proving the faithful flatness of the canonical homomorphisms from rings of Nash functions to rings of analytic functions, utilizing the vanishing of higher cohomology groups as guaranteed by Cartan's Theorem~B.

math.AG↗

arXiv2022

Spectral analysis for a class of bounded linear operators

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.

math.FA↗