Research Articles

P-Adic Numbers, Ultrametric Analysis, and Applications

, Volume 6, Issue 3, pp 171-187

Spectral analysis for finite rank perturbations of diagonal operators in non-archimedean Hilbert space

  • T. DiaganaAffiliated withDepartment of Mathematics, Howard University Email author 
  • , R. KerbyAffiliated withDepartment of Mathematics, Morgan State University
  • , TeyLama H. MiabeyAffiliated withDepartment of Mathematics, Howard University
  • , F. RamarosonAffiliated withDepartment of Mathematics, Howard University

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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 1v 1 + u 2v 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.

Key words

spectral analysis diagonal operator finite rank operator eigenvalue spectrum essential spectrum non-archimedean Hilbert space Fredholm operator completely continuous operators