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

  • T. Diagana
  • R. Kerby
  • TeyLama H. Miabey
  • F. Ramaroson
Research Articles

DOI: 10.1134/S2070046614030017

Cite this article as:
Diagana, T., Kerby, R., Miabey, T.H. et al. P-Adic Num Ultrametr Anal Appl (2014) 6: 171. doi:10.1134/S2070046614030017

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 = u1v1 + u2v2 + … + umvm 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 analysisdiagonal operatorfinite rank operatoreigenvaluespectrumessential spectrumnon-archimedean Hilbert spaceFredholm operatorcompletely continuous operators

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  • T. Diagana
    • 1
  • R. Kerby
    • 2
  • TeyLama H. Miabey
    • 1
  • F. Ramaroson
    • 1
  1. 1.Department of MathematicsHoward UniversityWashington, D.C.USA
  2. 2.Department of MathematicsMorgan State UniversityBaltimore, MarylandUSA