Spectral analysis for finite rank perturbation of diagonal operator in non-archimedean Banach space of countable type

Abstract

In this paper we are concerned with the spectral analysis for the classes of finte rank perturbations of diagonal operators in the form A = D+F where D is a diagonal operator and F = u’1 ⊗v’1+...+u’m ⊗vm is an operator of finite rank in the non-archimedean Banach space of countable type. We compute the spectrum of A using the theory of Fredholm operators in non archimedean setting and the concept of essential spectrum for linear operators.