Jaramillo Aguado, Jesús ÁngelPrieto Yerro, M. Ángeles2023-06-202023-06-201993-060002-993910.2307/2160323https://hdl.handle.net/20.500.14352/57615We 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.engjournal articlehttp://www.ams.org/restricted access517.518.235Tight algebrassuper-reflexive Banach spaceequivalent uniformly convex norm-spaceweak-polynomial convergence for sequences implies the norm convergenceweak polynomial convergence for sequences is different from the weakconvergencedual Banach spaceapproximation propertyuniform algebranot weakly compact Hankel-type operatorAnálisis funcional y teoría de operadores