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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Weak-polynomial convergence on a Banach space


Authors: J. A. Jaramillo and A. Prieto
Journal: Proc. Amer. Math. Soc. 118 (1993), 463-468
MSC: Primary 46B99; Secondary 46G20, 46J15
MathSciNet review: 1126196
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1126196-0
PII: S 0002-9939(1993)1126196-0
Article copyright: © Copyright 1993 American Mathematical Society