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Abstract:

We give a characterization of composition operators between algebras of analytic functions on a Banach space. We show (under fairly general conditions) that they are precisely the multiplicative operators that are transposes of operators of between the preduals of the algebras. The special cases of H ∞(U) and Hb(U) are considered. In these cases, the composition operators are those which are pointwise-to-pointwise continuous and/or τ0-to-τ0 continuous (where τ0 is the compact-open topology). We obtain Banach-Stone-type theorems for these algebras.

Registro:

Documento: Artículo
Título:A characterization of composition operators on algebras of analytic functions
Autor:Carando, D.
Filiación:Departamento de Matemática - Pab. I, Facultad de Ciencias Exactas Y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Composition operators; Holomorphic functions; Linearization of functions
Año:2008
Volumen:51
Número:2
Página de inicio:305
Página de fin:313
DOI: http://dx.doi.org/10.1017/S0013091506001143
Título revista:Proceedings of the Edinburgh Mathematical Society
Título revista abreviado:Proc. Edinburgh Math. Soc.
ISSN:00130915
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00130915_v51_n2_p305_Carando

Referencias:

  • ARON, R., GALINDO, P., LINDSTRÖM, M., Compact homomorphisms between algebras of analytic functions (1997) Studia Math, 123, pp. 235-247
  • BONET, J., FRIZ, M., Weakly compact composition operators on locally convex spaces (2002) Math. Nachr, 245, pp. 26-44
  • BONET, J., DOMAŃSKI, P., LINDSTRÖM, M., TASKINEN, J., Composition operators between wighted Banach spaces of analytic functions (1998) J. Austral. Math. Soc. A, 64, pp. 101-118
  • CARANDO, D., ZALDUENDO, I., Linearization of functions (2004) Math. Ann, 328, pp. 683-700
  • CARANDO, D., GARCÍA, D., MAESTRE, M., Homomorphisms and composition operators on algebras of analytic functions of bounded type (2005) Adv. Math, 197, pp. 607-629
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  • GARCÍA, D., MAESTRE, M., SEVILLA, P., Composition operators on weighted spaces of holomorphic functions on Banach spaces (2004) Ann. Acad. Sci. Fenn. Math, 29, pp. 81-98
  • KAUP, W., UPMEIER, H., Banach spaces with biholomorphically equivalent unit balls are isomorphic (1976) Proc. Am. Math. Soc, 58, pp. 129-133
  • MUJICA, J., Linearization of bounded holomorphic mappings on Banach spaces (1991) Trans. Am. Math. Soc, 324, pp. 867-887
  • MUJICA, J., Linearization of holomorphic mappings of bounded type (1992) Progress in functional analysis, pp. 149-162. , North-Holland, Amsterdam
  • TASKINEN, J., Compact composition operators on general weighted spaces (2001) Houston J. Math, 27, pp. 203-218
  • VIEIRA, D., Theorems of Banach-Stone type for algebras of holomorphic functions on infinite dimensional spaces (2006) Math. Proc. R. Irish Acad. A, 106, pp. 97-113

Citas:

---------- APA ----------
(2008) . A characterization of composition operators on algebras of analytic functions. Proceedings of the Edinburgh Mathematical Society, 51(2), 305-313.
http://dx.doi.org/10.1017/S0013091506001143
---------- CHICAGO ----------
Carando, D. "A characterization of composition operators on algebras of analytic functions" . Proceedings of the Edinburgh Mathematical Society 51, no. 2 (2008) : 305-313.
http://dx.doi.org/10.1017/S0013091506001143
---------- MLA ----------
Carando, D. "A characterization of composition operators on algebras of analytic functions" . Proceedings of the Edinburgh Mathematical Society, vol. 51, no. 2, 2008, pp. 305-313.
http://dx.doi.org/10.1017/S0013091506001143
---------- VANCOUVER ----------
Carando, D. A characterization of composition operators on algebras of analytic functions. Proc. Edinburgh Math. Soc. 2008;51(2):305-313.
http://dx.doi.org/10.1017/S0013091506001143