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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On James' quasi-reflexive Banach space


Authors: P. G. Casazza, Bor Luh Lin and R. H. Lohman
Journal: Proc. Amer. Math. Soc. 67 (1977), 265-271
MSC: Primary 46B15
DOI: https://doi.org/10.1090/S0002-9939-1977-0458129-5
MathSciNet review: 0458129
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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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DOI: https://doi.org/10.1090/S0002-9939-1977-0458129-5
Keywords: Basic sequences, projections, reflexive subspaces
Article copyright: © Copyright 1977 American Mathematical Society