Geodesic
Spectral analysis for rank one perturbations of diagonal operators in non-archimedean Hilbert space
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 3, pp. 385-400.

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The paper is concerned with the spectral analysis for the class of linear operators $A = D_\lambda + X \otimes Y$ in non-archimedean Hilbert space, where $D_\lambda$ is a diagonal operator and $X \otimes Y$ is a rank one operator. The results of this paper turn out to be a generalization of those results obtained by Diarra.
Classification : 42A75, 42A85, 44A35
Keywords: spectral analysis; diagonal operator; rank one operator; eigenvalue; spectrum; non-archimedean Hilbert space 
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     title = {Spectral analysis for rank one perturbations of diagonal operators in non-archimedean {Hilbert} space},
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Diagana, Toka; McNeal, George D. Spectral analysis for rank one perturbations of diagonal operators in non-archimedean Hilbert space. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 3, pp. 385-400. http://geodesic.mathdoc.fr/item/CMUC_2009__50_3_a5/