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Extremely weakly unconditionally convergent series

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Abstract

It is proved that if Σ ∞ i=1 X i is a non-convergent series in a Banach spaceX such that Σ ∞ i=1 |f(X i )|<∞ for all extreme pointsf of the unit ball ofX*, thenX contains a subspace isomorphic toc 0, improving a result of Bessaga and Pelczynski. The proof uses Fonf’s result that Lindenstrauss-Phelps spaces contain isomorphs ofc 0.

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Authors and Affiliations

  1. Department of Mathematics, The University of Texas, 78712, Austin, TX, USA

    John Elton

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  1. John Elton
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Supported in part by NSF-MCS-8002393.

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Elton, J. Extremely weakly unconditionally convergent series. Israel J. Math. 40, 255–258 (1981). https://doi.org/10.1007/BF02761366

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  • DOI: https://doi.org/10.1007/BF02761366

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