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Abstract:

Let f be a function in the Douglas algebra A and let I be a finitely generated ideal in A. We give an estimate for the distance from f to I that allows us to generalize a result obtained by Bourgain for H∞ to arbitrary Douglas algebras.

Registro:

Documento: Artículo
Título:An upper bound for the distance to finitely generated ideals in Douglas algebras
Autor:Gorkin, P.; Mortini, R.; Suàrez, D.
Filiación:Department of Mathematics, Bucknell University, Lewisburg, PA 17837, United States
Departamento de Matemática, Facultad de Cs. Exactas y Naturales, Ciudad Universitaria, (1428) Núñez, Cap. Fed., Argentina
Dept. de Mathématiques, Université de Metz, Ile du Saulcy, F-57045 Metz, France
Palabras clave:Douglas algebras; Maximal ideal space
Año:2001
Volumen:148
Número:1
Página de inicio:23
Página de fin:36
DOI: http://dx.doi.org/10.4064/sm148-1-3
Título revista:Studia Mathematica
Título revista abreviado:Stud. Math.
ISSN:00393223
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393223_v148_n1_p23_Gorkin

Referencias:

  • Axler, S., Factorization of L∞ functions (1977) Ann. of Math., 106, pp. 567-572
  • Bourgain, J., On finitely generated closed ideals in H∞(double-struck D) (1985) Ann. Inst. Fourier (Grenoble), 35 (4), pp. 163-174
  • Carleson, L., Interpolations by bounded analytic functions and the corona problem (1962) Ann. of Math., 76, pp. 547-559
  • Chang, S.-Y., A characterization of Douglas algebras (1976) Acta Math., 137, pp. 81-90
  • Dahlberg, B., Approximation of harmonic functions (1980) Ann. Inst. Fourier (Grenoble), 30 (2), pp. 97-107
  • Garnett, J.B., (1981) Bounded Analytic Functions, , Academic Press, New York
  • Gorkin, P., Mortini, R., A survey of closed ideals in familiar function algebras (1998) Contemp. Math., 232, pp. 161-170. , Function Spaces Edwardsville, IL, Amer. Math. Soc., Providence, RI
  • Guillory, C., Sarason, D., Division in H∞ + C (1981) Michigan Math. J., 28, pp. 173-181
  • Hoffman, K., (1962) Banach Spaces of Bounded Analytic Functions, , Prentice-Hall, Englewood Cliffs, NJ
  • Izuchi, K., Izuchi, Y., Inner functions and division in Douglas algebras (1986) Michigan Math. J., 33, pp. 435-443
  • Jones, P., Carleson measures and the Fefferman-Stein decomposition of BMO(ℝ) (1980) Ann. of Math., 111, pp. 197-208
  • Marshall, D.E., Subalgebras of L∞ containing H∞ (1976) Acta Math., 137, pp. 91-98
  • Rao, K.V.R., On a generalized corona problem (1967) J. Anal. Math., 18, pp. 277-278
  • Stout, E.L., (1971) The Theory of Uniform Algebras, , Bogden and Quigley, Belmont, CA
  • Wolff, T.H., Two algebras of bounded analytic functions (1982) Duke Math. J., 49, pp. 321-328

Citas:

---------- APA ----------
Gorkin, P., Mortini, R. & Suàrez, D. (2001) . An upper bound for the distance to finitely generated ideals in Douglas algebras. Studia Mathematica, 148(1), 23-36.
http://dx.doi.org/10.4064/sm148-1-3
---------- CHICAGO ----------
Gorkin, P., Mortini, R., Suàrez, D. "An upper bound for the distance to finitely generated ideals in Douglas algebras" . Studia Mathematica 148, no. 1 (2001) : 23-36.
http://dx.doi.org/10.4064/sm148-1-3
---------- MLA ----------
Gorkin, P., Mortini, R., Suàrez, D. "An upper bound for the distance to finitely generated ideals in Douglas algebras" . Studia Mathematica, vol. 148, no. 1, 2001, pp. 23-36.
http://dx.doi.org/10.4064/sm148-1-3
---------- VANCOUVER ----------
Gorkin, P., Mortini, R., Suàrez, D. An upper bound for the distance to finitely generated ideals in Douglas algebras. Stud. Math. 2001;148(1):23-36.
http://dx.doi.org/10.4064/sm148-1-3