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 

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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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