Spectral analysis for finite rank perturbations of diagonal operators in non-archimedean Hilbert space
Toka Diagana, Rodney Kerby, Teylama Miabey, François Ramaroson · P-Adic Numbers Ultrametric Analysis and Applications · 2014
In this paper we are concerned with the spectral analysis for some classes of finite rank perturbations of diagonal operators in the form, A = D + F, where D is a diagonal operator and F = u 1 ⊗ v 1 + u 2 ⊗ v 2 + … + u m ⊗ v m is an operator of finite rank in the non-archimedean Hilbert space $\mathbb{E}_\omega $ . Using the theory of Fredholm operators in the non-archimedean setting and the concept of essential spectrum for linear operators, we compute the spectrum of A. A few examples are given at the end of the paper to illustrate our main results.