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Construction of the functional model of B. S.-Nagy-C. Foias

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Abstract

Methodological paper: quick and simple construction of the Nagy—Foias functional model, using only elementary information about Hilbert spaces and operators on them. A formula is derived for a characteristic function. The account is based on an idea of B. S. Pavlov (Izv. Akad. Nauk SSSR, Ser. Mat.,39, No. 1, 123–148 (1975)) on symmetrization of the notation for a model space.

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Literature cited

  1. B. Szökefalvi-Nagy, “On Schäffer's construction of unitary dilations,” Ann. Univ. Budapest, Sect. Math.,3–4, 343–346 (1960/61).

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  2. J. J. Schäffer, “On unitary dilations of contractions,” Proc. Am. Math. Soc.,6, 322 (1955).

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  3. B. S. Pavlov, “Conditions for separability of spectral components of a dissipative operator,” Izv. Akad. Nauk SSSR, Ser. Mat.,39, No. 1, 123–148 (1975).

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Authors
  1. V. I. Vasyunin
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 73, pp. 16–23, 1977.

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Vasyunin, V.I. Construction of the functional model of B. S.-Nagy-C. Foias. J Math Sci 34, 2028–2033 (1986). https://doi.org/10.1007/BF01741576

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  • DOI: https://doi.org/10.1007/BF01741576

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