Llavona, José G. and Joaquín M., Gutiérrez and González, Manuel
*Polynomial continuity on l(1).*
Proceedings of the American Mathematical Society, 125
(5).
pp. 1349-1353.
ISSN 0002-9939

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Official URL: http://www.ams.org/journals/proc/1997-125-05/S0002-9939-97-03733-7/S0002-9939-97-03733-7.pdf

## Abstract

A mapping between Banach spaces is said to be polynomially continuous if its restriction to any bounded set is uniformly continuous for the weak polynomial topology. A Banach space X has property(RP) if given two bounded sequences (u(j)), (v(j)) subset of X; we have that Q(u(j)) - Q(v(j)) --> 0 for every polynomial Q on X whenever P(u(j) - v(j)) --> 0 for every polynomial P on XI i.e., the restriction of every polynomial on X to each bounded set is uniformly sequentially continuous for the weak polynomial topology. We show that property (RP) does not imply that every scalar valued polynomial on X must be polynomially continuous.

Item Type: | Article |
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Uncontrolled Keywords: | Polynomials on Banach spaces; Weak polynomial topology; Polynomials on l(1) |

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

ID Code: | 16256 |

References: | R. M. Aron, Y. S. Choi and J. G. Llavona, Estimates by polynomials, Bull. Austral. Math. Soc. 52 (1995), 475-486. CMP 96:03 R. M. Aron and J. B. Prolla, Polynomial approximation of diferentiable functions on Banach spaces, J. Reine Angew. Math. 313 (1980), 195-216. MR 81c:41078 T. K. Carne, B. Cole and T. W. Gamelin, A uniform algebra of analytic functions on a Banach space, Trans. Amer. Math. Soc. 314 (1989), 639-659. MR 90i:46098 A. M. Davie and T. W. Gamelin, A theorem on polynomial-star approximation, Proc. Amer. Math. Soc. 106 (1989), 351-356. MR 89k:46023 J. Diestel, Sequences and Series in Banach Spaces, Graduate Texts in Math. 92, Springer, Berlin 1984. MR 85i:46020 J. Mujica, Complex Analysis in Banach Spaces, Math. Studies 120, North-Holland, Amster- dam 1986. MR 88d:46084 |

Deposited On: | 10 Sep 2012 09:13 |

Last Modified: | 07 Feb 2014 09:25 |

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