Geodesic
A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces
Studia Mathematica, Tome 127 (1998) no. 1, pp. 65-80

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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.
DOI : 10.4064/sm-127-1-65-80

G. Androulakis 1

1 
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G. Androulakis. A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces. Studia Mathematica, Tome 127 (1998) no. 1, pp. 65-80. doi: 10.4064/sm-127-1-65-80

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