Abstract
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.
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Diagana, T., Kerby, R., Miabey, T.H. et al. Spectral analysis for finite rank perturbations of diagonal operators in non-archimedean Hilbert space. P-Adic Num Ultrametr Anal Appl 6, 171–187 (2014). https://doi.org/10.1134/S2070046614030017
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DOI: https://doi.org/10.1134/S2070046614030017