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Jaramillo Aguado, Jesús Ángel and Prieto Yerro, M. Ángeles
(1993)
*Weak-Polynomial Convergence on a Banach Space.*
Proceedings of the American Mathematical Society, 118
(2).
pp. 463-468.
ISSN 0002-9939

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## Abstract

We show that any super-reflexive Banach space is a LAMBDA-space (i.e., the weak-polynomial convergence for sequences implies the norm convergence). We introduce the notion Of kappa-space (i.e., a Banach space where the weak-polynomial convergence for sequences is different from the weak convergence) and we prove that if a dual Banach space Z is a kappa-space with the approximation property, then the uniform algebra A(B) on the unit ball of Z generated by the weak-star continuous polynomials is not tight.

Item Type: | Article |
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Uncontrolled Keywords: | Tight algebras; super-reflexive Banach space; equivalent uniformly convex norm; -space; weak-polynomial convergence for sequences implies the norm convergence; -space; weak polynomial convergence for sequences is different from the weakconvergence; dual Banach space; approximation property; uniform algebra; not weakly compact Hankel-type operator |

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

ID Code: | 16788 |

Deposited On: | 22 Oct 2012 09:24 |

Last Modified: | 27 Jul 2018 07:32 |

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