Banach spaces of polynomials without copies of $l^ 1$
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- by Manuel Valdivia PDF
- Proc. Amer. Math. Soc. 123 (1995), 3143-3150 Request permission
Abstract:
Let X be a Banach space. For a positive integer m, let ${\mathcal {P}_{{w^ \ast }}}{(^m}{X^ \ast })$ denote the Banach space formed by all m-homogeneous polynomials defined on ${X^ \ast }$ whose restrictions to the closed unit ball $B({X^ \ast })$ of ${X^ \ast }$ are continuous for the weak-star topology. For each one of such polynomials, its norm will be the supremum of the absolute value in $B({X^ \ast })$. In this paper the bidual of ${\mathcal {P}_{{w^ \ast }}}{(^m}{X^ \ast })$ is constructed when this space does not contain a copy of ${l^1}$. It is also shown that, whenever X is an Asplund space, ${\mathcal {P}_{{w^ \ast }}}{(^m}{X^ \ast })$ is also Asplund.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 3143-3150
- MSC: Primary 46G20; Secondary 46B20
- DOI: https://doi.org/10.1090/S0002-9939-1995-1273528-0
- MathSciNet review: 1273528