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Weak-Polynomial Convergence on a Banach Space

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
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
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Deposited On:22 Oct 2012 09:24
Last Modified:07 Feb 2014 09:35

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