Finitely nonreflexive Banach spaces

Wójtowicz, Marek

doi:10.1090/S0002-9939-1989-0949882-0

Finitely nonreflexive Banach spaces
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Proc. Amer. Math. Soc. 106 (1989), 961-965 Request permission

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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