Spectral analysis for finite rank perturbations of diagonal operators in non-archimedean Hilbert space |
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Authors: | T. Diagana R. Kerby TeyLama H. Miabey F. Ramaroson |
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Affiliation: | 1. Department of Mathematics, Howard University, 2441 6th Street N.W., Washington, D.C., 20059, USA 2. Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, Maryland, 21251, USA
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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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