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Integral Equations and Operator Theory

, Volume 2, Issue 1, pp 48–61 | Cite as

On analytic equivalence of operator polynomials

  • Leiba Rodman
Article

Abstract

It is proved that analytic equivalence of monic operator polynomials implies the similarity of their linearizations. In particular, linear operator polynomials λI-X and λI-Y are analytically equivalent if and only if X and Y are similar.

Keywords

Linear Operator Operator Polynomial Monic Operator Linear Operator Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Gohberg, I.C., Kaashoek, M.A. and Lay, D.C.: Spectral classification of operators and operator functions, Bull. Amer. Math. Soc. 82 (1976), 587–589.Google Scholar
  2. [2]
    Gohberg, I., Lancaster, P. and Rodman, L.: Spectral analysis of matrix polynomials, I. Canonical forms and divisors, Lin. Alg. and Appl. 20 (1978), 1–44.Google Scholar
  3. [3]
    Gohberg, I., Lancaster, P. and Rodman, L.: Spectral analysis of matrix polynomials, II. The resolvent form and spectral divisors, Lin. Alg. and Appl. 21 (1978), 65–88.Google Scholar
  4. [4]
    Gohberg, I., Lancaster, P. and Rodman, L.: Representations and divisibility of operator polynomials, Can. J. Math. 30 (1978), 1045–1069.Google Scholar
  5. [5]
    Gohberg, I. and Leiterer, J.: General theorem on canonical factorization of operator functions with respect to a contour, Matem. Issled., VII:3 (25) (1972), 87–134 (Russian).Google Scholar
  6. [6]
    Gohberg, I., Lerer, L. and Rodman, L.: On canonical factorization of operator polynomials, spectral divisors and Toeplitz matrices, Integral Equations and Operator Theory, 1/2 (1978), 176–214.Google Scholar
  7. [7]
    Gohberg, I., Lerer, L. and Rodman, L.: Stable factorization of operator polynomials and spectral divisors simply behaved at infinity, Tel-Aviv University, preprint, 1978.Google Scholar

Copyright information

© Birkhäuser Verlag 1979

Authors and Affiliations

  • Leiba Rodman
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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