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Abstract:

If b ∈ B(H∞), the unit ball of H∞, then the de Branges-Rovnyak space H(b) is a Hilbert space contained contractively in H2 that is invariant by the backward shift operator S*. When b is an inner function, the invariant subspaces of H(b) are given by Beurling's theorem and when b is not an extreme point of B(H∞), they were characterized by Sarason. We characterize the invariant subspaces of H(b) when b is any extreme point of B(H∞).

Registro:

Documento: Artículo
Título:Backward shift invariant spaces in H2
Autor:Suárez, D.
Filiación:Departamento de Matemática, Fac. de Cie. Exactas y Naturales, Ciudad Universitaria, Capital Federal, Argentina
Año:1997
Volumen:46
Número:2
Página de inicio:593
Página de fin:619
Título revista:Indiana University Mathematics Journal
Título revista abreviado:Indiana Univ. Math. J.
ISSN:00222518
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222518_v46_n2_p593_Suarez

Referencias:

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  • Ball, J.A., Lubin, A., On a class of contractive perturbations of restricted shifts (1976) Pacific J. Math., 63, pp. 309-323
  • Clark, D.N., One dimensional perturbations of restricted shifts (1972) J. Analyse Math., 25, pp. 169-191
  • Cima, J.A., McGregor, T.H., Cauchy transforms of measures and univalent functions (1978) Lectures Notes in Math., 1275, pp. 78-88. , Springer, Berlin
  • De Branges, L., Rovnyak, J., (1966) Square Summable Power Series, , Holt, Reinhart and Winston, New York
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  • Hoffman, K., (1962) Banach Spaces of Bounded Analytic Functions, , Prentice Hall, Englewood Cliffs, New Jersey
  • Lotto, B.A., Sarason, D., Multiplicative structure of de Branges's spaces (1991) Rev. Mat. Iberoamericana, 7, pp. 183-220
  • Nikolskh, N.K., Vasyunin, V.I., Notes on two function models (1986) Proceedings of the Symposium on the Occasion of the Proof of the Bieberbach Conjecture, pp. 113-141. , Math. Surveys, Amer. Math. Soc., Providence
  • Sarason, D., Generalized interpolation in H∞ (1967) Trans. Amer. Math. Soc., 127, pp. 179-203
  • Sarason, D., (1995) Sub-Hardy Hilbert Spaces in the Unit Disk, , John Wiley & Sons, Inc., New York
  • Sarason, D., Shift-invariant spaces from the Brangesian point of view (1986) Proceedings of the Symposium on the Occasion of the Proof of the Bieberbach Conjecture, pp. 153-166. , Math. Surveys, Amer. Math. Soc., Providence
  • Sarason, D., Doubly shift-invariant spaces in H2 (1986) J. Operator Theory, 16, pp. 75-97
  • Suárez, D., Multipliers of de Branges-Rovnyak spaces in H2 (1995) Rev. Mat. Iberoamericana, 11, pp. 375-415
  • Suárez, D., Closed commutants of the backward shift operator (1997) Pacific J. Math., 179, pp. 371-396
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Citas:

---------- APA ----------
(1997) . Backward shift invariant spaces in H2. Indiana University Mathematics Journal, 46(2), 593-619.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222518_v46_n2_p593_Suarez [ ]
---------- CHICAGO ----------
Suárez, D. "Backward shift invariant spaces in H2" . Indiana University Mathematics Journal 46, no. 2 (1997) : 593-619.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222518_v46_n2_p593_Suarez [ ]
---------- MLA ----------
Suárez, D. "Backward shift invariant spaces in H2" . Indiana University Mathematics Journal, vol. 46, no. 2, 1997, pp. 593-619.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222518_v46_n2_p593_Suarez [ ]
---------- VANCOUVER ----------
Suárez, D. Backward shift invariant spaces in H2. Indiana Univ. Math. J. 1997;46(2):593-619.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222518_v46_n2_p593_Suarez [ ]