Let (x_n) be a sequence in a Banach space X which does not converge in norm, and let E be an isomorphically precisely norming set for X such that (*) ∑_n |x*(x_{n+1} - x_n)| < ∞, ∀x* ∈ E. Then there exists a subsequence of (x_n) which spans an isomorphically polyhedral Banach space. It follows immediately from results of V. Fonf that the converse is also true: If Y is a separable isomorphically polyhedral Banach space then there exists a normalized M-basis (x_n) which spans Y and there exists an isomorphically precisely norming set E for Y such that (*) is satisfied. As an application of this subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces we obtain a strengthening of a result of J. Elton, and an Orlicz-Pettis type result.
@article{bwmeta1.element.bwnjournal-article-smv127i1p65bwm,
author = {G. Androulakis},
title = {A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces},
journal = {Studia Mathematica},
volume = {129},
year = {1998},
pages = {65-80},
zbl = {0911.46008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv127i1p65bwm}
}
Androulakis, G. A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces. Studia Mathematica, Tome 129 (1998) pp. 65-80. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv127i1p65bwm/
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