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Quasisimilarity of model contractions with unequal defects

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Abstract

Let Tθ and Tϕ be C10 contractions with characteristic functions θ∈H (ℂn→ℂn+1), ϕ∈H (ℂm→ℂm+1). The fundamental result is: Tθ and Tϕ are quasisimilar if and only if

The paper contains an analysis of this condition; examples are given.

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Literature cited

  1. 1.

    V. I. Vasyunin and N. K. Nikol'skii, “Control subspaces of minimal dimension. Elementary introduction. Discotheca,” J. Sov. Math.,22, No. 6 (1983).

  2. 2.

    J. B. Garnett, Bounded Analytic Functions, Academic Press, New York (1981).

  3. 3.

    N. K. Nikol'skii, Lectures on the Shift Operator [in Russian], Nauka, Moscow (1980).

  4. 4.

    B. Sz.-Nagy and C. Foias, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam (1970).

  5. 5.

    H. Bercovici, C. Foias, and B. Sz.-Nagy, “Complements a l'etude des operateurs de classe Co. III,” Acta Sci. Math. (Szeged),37, No. 3–4, 313–322 (1975).

  6. 6.

    E. A. Nordgren, “The ring N+ is not adequate,” Acta Sci. Math. (Szeged),36, No. 1–2, 203–204 (1974).

  7. 7.

    B. Sz.-Nagy and C. Foias, “Modéle de Jordan pour une classe d'opérateurs de l'éspace de Hilbert,” Acta Sci. Math. (Szeged),31, No. 1–2, 91–115 (1970).

  8. 8.

    B. Sz.-Nagy and C. Foias, “Jordan model for contractions of class C.o,” Acta Sci. Math. (Szeged),36, No. 3–4, 305–322 (1974).

  9. 9.

    Pei Yuan Wu, “Quasisimilarity of weak contractions,” Proc. Am. Math. Soc.,69, 277–282 (1978).

  10. 10.

    Pei Yuan Wu, “Jordan model for weak contractions,” Acta Sci. Math. (Szeged),40, No. 1–2, 189–196 (1978).

  11. 11.

    Pei Yuan Wu, “On contractions of class C1,” Acta Sci. Math. (Szeged),42, No. 1–2, 205–210 (1980).

  12. 12.

    Pei Yuan Wu, “C.o contractions: cyclic vectors, commutants and Jordan models,” J. Operator Theory,5, No. 1, 53–62 (1981).

  13. 13.

    Pei Yuan Wu, “When is a contraction quasi-similar to an isometry?” Acta Sci. Math. (Szeged),44, No. 1–2, 151–155 (1982).

  14. 14.

    Pei Yuan Wu, “Which C.o contraction is quasisimilar to its Jordan model?” Acta Sci. Math. (Szeged),47, No. 3–4, 449–455 (1984).

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 149, pp. 24–37, 1986.

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Vasyunin, V.I., Makarov, N.G. Quasisimilarity of model contractions with unequal defects. J Math Sci 42, 1550–1561 (1988). https://doi.org/10.1007/BF01665041

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