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Finitely nonreflexive Banach spaces


Author: Marek Wójtowicz
Journal: Proc. Amer. Math. Soc. 106 (1989), 961-965
MSC: Primary 46B10; Secondary 46B25
DOI: https://doi.org/10.1090/S0002-9939-1989-0949882-0
MathSciNet review: 949882
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Abstract: A Banach space $ X$ is said to be finitely nonreflexive if for some $ n \geq 1$ the space $ {H_n}(X)$ is reflexive with $ \dim {H_n}(X) \geq 1$, where $ {H_0}(X) = X$, and $ {H_{n + 1}}(X) = {H_n}{(X)^{**}}/{H_n}(X)$. A simple construction of (pairwise nonisomorphic) finitely nonreflexive separable Banach spaces which are both nonisomorphic to their Cartesian squares and isomorphic to their biduals is presented.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0949882-0
Keywords: Biduals of Banach spaces, quasi-reflexive spaces
Article copyright: © Copyright 1989 American Mathematical Society

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