Weak-polynomial convergence on a Banach space
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- by J. A. Jaramillo and A. Prieto
- Proc. Amer. Math. Soc. 118 (1993), 463-468
- DOI: https://doi.org/10.1090/S0002-9939-1993-1126196-0
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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.References
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Bibliographic Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 118 (1993), 463-468
- MSC: Primary 46B99; Secondary 46G20, 46J15
- DOI: https://doi.org/10.1090/S0002-9939-1993-1126196-0
- MathSciNet review: 1126196