On analytic equivalence of operator polynomials
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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.
KeywordsLinear Operator Operator Polynomial Monic Operator Linear Operator Polynomial
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- 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
- 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
- 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
- Gohberg, I., Lancaster, P. and Rodman, L.: Representations and divisibility of operator polynomials, Can. J. Math. 30 (1978), 1045–1069.Google Scholar
- 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
- 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
- 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