Positivity

, Volume 9, Issue 1, pp 97–114 | Cite as

p -Diagonally Dominant Symmetric Operators

Article

Abstract

The existence of ℓ p -universal diagonally dominant symmetric liner operators on separable Hilbert spaces is discussed. Also, properties of these operators and their characterization in terms of their spectra are investigated.

Keywords

diagonally dominant symmetric operator definite operator separable Hilbert space numerical range Lagrange’s multiplier 

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References

  1. 1.
    Agranovich, Y., Ya,  1998The theory of operators with dominant main diagonal IPositivity2153164Google Scholar
  2. 2.
    Farid, F.O. 1991Spectral properties of perturbed linear operators and their application to infinite matricesProc. Am. Math. Soc11210131022Google Scholar
  3. 3.
    Farid, F.O. 1995Criteria for invertibility of diagonally dominant matricesLinear Algebra Appl.2156393Google Scholar
  4. 4.
    Gershgorin, S. 1931Uber die abgrenzung der eigenwerte einer matrixlzv. Akad. Nauk. S.S.S.R.7749754Google Scholar
  5. 5.
    Halmos, P.R. 1982A Hilbert Space Problem BookSpringerNew YorkGoogle Scholar
  6. 6.
    Hanani, H., Netanyahu, E., Reichaw, M. 1968Eigen values of infinite matricesColloq. Math.XIX89101Google Scholar
  7. 7.
    Horn, R.A., Johnson, C.R. 1985Matrix AnalysisCambridge University PressNew YorkGoogle Scholar
  8. 8.
    Kantorovich, L.V. 1948Functional analysis and applied mathematicsUspehi Mathematicheskih Nauk3687185(Russ)Google Scholar
  9. 9.
    Shivakumar, P.N., Williams, J.J., Rudraiah, N. 1987Eigenvalues for infinite matricesLinear Algebra Appl.963563Google Scholar
  10. 10.
    Taylor, A. E. and Lay, D. C.: Introduction to Functional Analysis, Reprint ed., Krieger Publishing Company, 1986.Google Scholar
  11. 11.
    Taussky, O. 1949A recurring theorem on determinantsAm. Math. Monthly56672676Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.KelownaCanada

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