Spectral analysis for finite rank perturbation of diagonal operator in non-archimedean Banach space of countable type
Keywords:non-archimedean Banach spaces, diagonal and Fredholm operators, spectrum of operators
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.
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