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Aron, R.M.; Carando, D.; Gamelin, T.W.; Lassalle, S.; Maestre, M. "Cluster values of analytic functions on a Banach space" (2012) Mathematische Annalen. 353(2):293-303
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Abstract:

We investigate uniform algebras of bounded analytic functions on the unit ball of a complex Banach space. We prove several cluster value theorems, relating cluster sets of a function to its range on the fibers of the spectrum of the algebra. These lead to weak versions of the corona theorem for ℓ 2 and for c 0. In the case of the open unit ball of c 0, we solve the corona problem whenever all but one of the functions comprising the corona data are uniformly approximable by polynomials in functions in c * 0. © 2011 Springer-Verlag.

Registro:

Documento: Artículo
Título:Cluster values of analytic functions on a Banach space
Autor:Aron, R.M.; Carando, D.; Gamelin, T.W.; Lassalle, S.; Maestre, M.
Filiación:Department of Mathematical Sciences, Kent State University, Kent, OH 44242, United States
Departamento de Matemática, Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, CONICET, 1428 Buenos Aires, Argentina
Department of Mathematics, UCLA, Los Angeles, CA 90095, United States
Departmento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, 6100 Burjasot, Valencia, Spain
Año:2012
Volumen:353
Número:2
Página de inicio:293
Página de fin:303
DOI: http://dx.doi.org/10.1007/s00208-011-0681-0
Título revista:Mathematische Annalen
Título revista abreviado:Math. Ann.
ISSN:00255831
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255831_v353_n2_p293_Aron

Referencias:

  • Aron, R.M., Cole, B., Gamelin, T., Spectra of algebras of analytic functions on a Banach space (1991) J. Reine. Angew. Math., 415, pp. 51-93
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  • Gamelin, T.W., Analytic functions on Banach spaces (1994) Complex Potential Theory (Montreal, P. Q., 1993), NATO Advanced Science Institustes Series C. Mathematical and Physical Sciences, 439, pp. 187-233. , Kluwer Academic Publisher, Dordrecht
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  • Mujica, J., Complex analysis in Banach spaces (2010) North-Holland Mathematics Studies, 120. , North-Holland, Amsterdam (1986) reprinted by Dover, Mineola
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  • Schark, I.J., Maximal ideals in an algebra of bounded analytic functions (1961) J. Math. Mech., 10, pp. 735-746

Citas:

---------- APA ----------
Aron, R.M., Carando, D., Gamelin, T.W., Lassalle, S. & Maestre, M. (2012) . Cluster values of analytic functions on a Banach space. Mathematische Annalen, 353(2), 293-303.
http://dx.doi.org/10.1007/s00208-011-0681-0
---------- CHICAGO ----------
Aron, R.M., Carando, D., Gamelin, T.W., Lassalle, S., Maestre, M. "Cluster values of analytic functions on a Banach space" . Mathematische Annalen 353, no. 2 (2012) : 293-303.
http://dx.doi.org/10.1007/s00208-011-0681-0
---------- MLA ----------
Aron, R.M., Carando, D., Gamelin, T.W., Lassalle, S., Maestre, M. "Cluster values of analytic functions on a Banach space" . Mathematische Annalen, vol. 353, no. 2, 2012, pp. 293-303.
http://dx.doi.org/10.1007/s00208-011-0681-0
---------- VANCOUVER ----------
Aron, R.M., Carando, D., Gamelin, T.W., Lassalle, S., Maestre, M. Cluster values of analytic functions on a Banach space. Math. Ann. 2012;353(2):293-303.
http://dx.doi.org/10.1007/s00208-011-0681-0