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

Abdelkhalek El Amrani, Aziz Blali, Mohamed Amine Taybi

• 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  is an operator of finite rank in the non archimedean Banach space of countable type. Using the theory of Fredholm operators in non archimedean setting and the concept of essential spectrum for linear operators, we compute the spectrum of A.