| This Dissertation is aimed at studying the spectral theory for linear operators in the form A = Dlambda + U ⊗ V on a non-archimedean Hilbert space, where Dlambda is a diagonal operator and U ⊗ V is a rank-one operator. Indeed, under some suitable assumptions, we will show that A is invertible. Next, we make extensive use of the inverse of A to compute the spectrum sigma(A) of A in the case when the valuation is not only of rank-one but also in the case of a Krull valuation. The results of this Dissertation turn out to be generalizations of those of Diarra, and Keller - Ochsenius. |
