On James’ quasi-reflexive Banach space

Casazza, P. G.; Lin, Bor Luh; Lohman, R. H.

doi:10.1090/S0002-9939-1977-0458129-5

On James’ quasi-reflexive Banach space
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by P. G. Casazza, Bor Luh Lin and R. H. Lohman PDF

Proc. Amer. Math. Soc. 67 (1977), 265-271 Request permission

Abstract:

In the James’ space J, there exist complemented reflexive subspaces which are not uniformly convexifiable and there are uncountably many mutually nonequivalent unconditional basic sequences in J each of which spans a complemented subspace of J. If $\{ {y_n}\}$ is a block basic sequence with constant coefficients of the unit vector basis of J, then its closed linear span $[{y_n}]$ is complemented in J and the space $[{y_n}]$ is either isomorphic to J or to ${(\Sigma _{n = 1}^\infty {J_{{t_n}}})_{{l_2}}}$ for some $\{ {t_n}\}$ where ${J_n} = [{e_1},{e_2}, \ldots ,{e_n}]$.

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