### Impacto

Llavona, José G. and Moraes, Luiza A.
(2004)
*The Aron-Berner extension for polynomials defined in the dual of a Banach space.*
Publications of the Research Institute for Mathematical Sciences, 40
(1).
pp. 221-230.
ISSN 0034-5318

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Official URL: http://www.ems-ph.org/journals/show_issue.php?issn=0034-5318&vol=40&iss=1

## Abstract

Let E = F' where F is a complex Banach space and let pi(1) : E" - E circle plus F-perpendicular to --> E be the canonical projection. Let P(E-n) be the space of the complex valued continuous n-homogeneous polynomials defined in E. We characterize the elements P is an element of P(E-n) whose Aron-Berner extension coincides with P circle pi(1). The case of weakly continuous polynomials is considered. Finally we also study the same problem for holomorphic functions of bounded type.

Item Type: | Article |
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Uncontrolled Keywords: | Homogeneous polynomials; Holomorphic functions; Weak star topology. |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 15976 |

References: | Aron, R. M., Weakly uniformly continuous and weakly sequentially continuous entire functions, Advances in Holomorphy, J. A. Barroso (Ed.), Math. Stud., 34, North Holland, Amsterdam (1979), 47-66. Aron, R. M. and Berner, P., A Hahn-Banach extension theorem for analytic mappings, Bull. Soc. Math. France, 106 (1978), 3-24. Aron, R. M., Boyd, C. and Choi, Y. S., Unique Hahn-Banach Theorems for spaces of homogeneous polynomials, J. Austral. Math. Soc., 70 (2001), 387-400. Aron, R. M., Hervés, C. and Valdivia, M., Weakly continuous mappings on Banach Spaces, J. Funct. Anal., 52 (1983), 189-204. Aron, R. M., Moraes, L. A. and Ryan, R., Factorization of holomorphic mappings in infinite dimensions, Math. Ann., 277(4) (1987), 617-628. Aron, R. M. and Prolla, J. B., Polynomial approximation of differentiable functions on Banach spaces, J. Reine Angew. Math., 313 (1980), 195-216. Aron, R. M. and Schottenloher, R. M., Compact holomorphic mappings on Banach spaces and approximation property, J. Funct. Anal., 21 (1976), 7-30. Davie, A. M. and Gamelin, T. W., A theorem on polynomial-star approximation, Proc. Amer. Math. Soc., 106 (1989), 351-356. Dineen, S., Holomorphy types on a Banach space, Studia Math. 34 (1977), 241-288. Complex Analysis on Infinite Dimensional Spaces, Springer Monogr. Math., Springer Verlag, London, Berlin, Heidelberg, 1999. Floret, K., Natural norms on symmetric tensor products of normed spaces, Proc. of II Int. Workshop on Functional Analysis at Trier University, Note Mat., 17 (1997),153-188. Gonzalez, M., Gutierrez, J. M. and Llavona, J. L., Polynomial continuity on l1, Proc. Amer. Math. Soc., 125(5) (1997), 1349-1353. Mujica, J., Complex Analysis in Banach Spaces, Math. Stud., 120, North Holland, Amsterdam, 1986. Zalduendo, I., A canonical extension for analytic functions on Banach spaces, Trans.Amer. Math. Soc., 320 (1990), 747-763. |

Deposited On: | 18 Jul 2012 08:49 |

Last Modified: | 06 Feb 2014 10:35 |

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