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Abstract:

Given a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type. We prove that, under very natural conditions satisfied by many usual classes of polynomials, the spectrum of this algebra "behaves" like the classical case of M b(E) (the spectrum of H b(E), the algebra of bounded type holomorphic functions). More precisely, we prove that can be endowed with a structure of Riemann domain over E′′ and that the extension of each -holomorphic function of bounded type in each connected component. We also prove a Banach-Stone type theorem for these algebras. © 2010 Universitat de Barcelona.

Registro:

Documento: Artículo
Título:Holomorphic functions and polynomial ideals on Banach spaces
Autor:Carando, D.; Dimant, V.; Muro, S.
Filiación:Departamento de Matemática, Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, Victoria, B1644BID Buenos Aires, Argentina
Palabras clave:Holomorphic functions; Polynomial ideals; Riemann domains over banach spaces
Año:2012
Volumen:63
Número:1
Página de inicio:71
Página de fin:91
DOI: http://dx.doi.org/10.1007/s13348-010-0025-5
Título revista:Collectanea Mathematica
Título revista abreviado:Collect. Math.
ISSN:00100757
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00100757_v63_n1_p71_Carando

Referencias:

  • Alencar, R., Multilinear mappings of nuclear and integral type (1985) Proc. Am. Math. Soc., 94, pp. 33-38
  • Aron, R.M., Weakly uniformly continuous and weakly sequentially continuous entire functions (1979) Advances in holomorphy (Proc. Sem. Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1977), pp. 47-66. , North-Holland Math. Studies 34, North-Holland, Amsterdam
  • Aron, R.M., Cole, B.J., Gamelin, T.W., Weak-star continuous analytic functions (1995) Can. J. Math., 47, pp. 673-683
  • Aron, R.M., Galindo, P., García, D., Maestre, M., Regularity and algebras of analytic functions in infinite dimensions (1996) Trans. Am. Math. Soc., 348, pp. 543-559
  • Aron, R.M., Hervés, C., Valdivia, M., Weakly continuous mappings on Banach spaces (1983) J. Funct. Anal., 52, pp. 189-204
  • Boyd, C., Lassalle, S., Decomposable symmetric mappings between infinite-dimensional spaces (2008) Ark. Mat., 46, pp. 7-29
  • Boyd, C., Ryan, R.A., Geometric theory of spaces of integral polynomials and symmetric tensor products (2001) J. Funct. Anal., 179, pp. 18-42
  • Carando, D., Extendible polynomials on Banach spaces (1999) J. Math. Anal. Appl., 233, pp. 359-372
  • Carando, D., Extendibility of polynomials and analytic functions on l p (2001) Studia Math., 145, pp. 63-73
  • Carando, D., Dimant, V., Duality in spaces of nuclear and integral polynomials, J (2000) Math. Anal. Appl., 241, pp. 107-121
  • Carando, D., Dimant, V., Muro, S., Hypercyclic convolution operators on Fréchet spaces of analytic functions (2007) J. Math. Anal. Appl., 336, pp. 1324-1340
  • Carando, D., Dimant, V., Muro, S., Coherent sequences of polynomial ideals on Banach spaces (2009) Math. Nachr., 282, pp. 1111-1133
  • Carando, D., Galicer, D., Extending polynomials in maximal and minimal ideals (2010) Publ. Res. Inst. Math. Sci., 46 (3), pp. 669-680
  • Carando, D., Galicer, D., Natural symmetric tensor norms, , (preprint)
  • Carando, D., Galicer, D., The symmetric Radon-Nikodym property for tensor norms (2010) J. Math. Anal. Appl., , doi: 10. 1016/j. jmaa. 2010. 09. 044
  • 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
  • Carando, D., Lassalle, S., E′ and its relation with vector-valued functions on E (2004) Ark. Mat., 42, pp. 283-300
  • Carando, D., Zalduendo, I., A Hahn-Banach theorem for integral polynomials (1999) Proc. Am. Math. Soc., 127, pp. 241-250
  • Davie, A.M., Gamelin, T.W., A theorem on polynomial-star approximation (1988) Proc. Am. Math. Soc., 106, pp. 351-356
  • Defant, A., Floret, K., (1993) Tensor Norms and Operator Ideals, 176. , North-Holland: North-Holland Mathematics Studies
  • Dimant, V., Galindo, P., Maestre, M., Zalduendo, I., Integral holomorphic functions (2004) Studia Math., 160, pp. 83-99
  • Dineen, S., (1999) Complex Analysis on Infinite Dimensional Spaces. Springer Monographs in Mathematics, , London: Springer
  • Dineen, S., Holomorphy types on a Banach space (1971) Studia Math., 39, pp. 241-288
  • Floret, K., Natural norms on symmetric tensor products of normed spaces (1997) Note Mat., 17, pp. 153-188
  • Floret, K., Minimal ideals of n-homogeneous polynomials on Banach spaces (2001) Results Math., 39, pp. 201-217
  • Floret, K., On ideals of n-homogeneous polynomials on Banach spaces (2002) Topological algebras with applications to differential geometry and mathematical physics (Athens, 1999), pp. 19-38. , University Athens, Athens
  • Floret, K., Hunfeld, S., Ultrastability of ideals of homogeneous polynomials and multilinear mappings on Banach spaces (2002) Proc. Am. Math. Soc., 130, pp. 1425-1435
  • Gupta, C.P., On the Malgrange theorem for nuclearly entire functions of bounded type on a Banach space (1970) Nederl. Akad. Wetensch. Proc. Ser. A73 = Indag. Math., 32, pp. 356-358
  • Harris, L.A., A Bernstein-Markov theorem for normed spaces (1997) J. Math. Anal. Appl., 208, pp. 476-486
  • Lassalle, S., Zalduendo, I., To what extent does the dual Banach space E′ determine the polynomials over E? (2000) Ark. Mat., 38, pp. 343-354
  • Moraes, L.A., The Hahn-Banach extension theorem for some spaces of n-homogeneous polynomials (1984) Functional Analysis: Surveys and Recent Results, III, 90, pp. 265-274. , (Paderborn, 1983). North-Holland Mathematics Studies, North-Holland
  • Mujica, J., Complex analysis in Banach spaces (1986) Holomorphic functions and domains of holomorphy in finite and infinite dimensions, 120. , North-Holland Mathematics Studies, North-Holland Publishing Co., Amsterdam
  • Nachbin, L., (1969) Topology on Spaces of Holomorphic Mappings. Ergebnisse Der Mathematik Und Ihrer Grenzgebiete, Band 47, , New York: Springer

Citas:

---------- APA ----------
Carando, D., Dimant, V. & Muro, S. (2012) . Holomorphic functions and polynomial ideals on Banach spaces. Collectanea Mathematica, 63(1), 71-91.
http://dx.doi.org/10.1007/s13348-010-0025-5
---------- CHICAGO ----------
Carando, D., Dimant, V., Muro, S. "Holomorphic functions and polynomial ideals on Banach spaces" . Collectanea Mathematica 63, no. 1 (2012) : 71-91.
http://dx.doi.org/10.1007/s13348-010-0025-5
---------- MLA ----------
Carando, D., Dimant, V., Muro, S. "Holomorphic functions and polynomial ideals on Banach spaces" . Collectanea Mathematica, vol. 63, no. 1, 2012, pp. 71-91.
http://dx.doi.org/10.1007/s13348-010-0025-5
---------- VANCOUVER ----------
Carando, D., Dimant, V., Muro, S. Holomorphic functions and polynomial ideals on Banach spaces. Collect. Math. 2012;63(1):71-91.
http://dx.doi.org/10.1007/s13348-010-0025-5