# A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces

Studia Mathematica (1998)

- Volume: 127, Issue: 1, page 65-80
- ISSN: 0039-3223

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topAndroulakis, G.. "A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces." Studia Mathematica 127.1 (1998): 65-80. <http://eudml.org/doc/216460>.

@article{Androulakis1998,

abstract = {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.},

author = {Androulakis, G.},

journal = {Studia Mathematica},

keywords = {isomorphically polyhedral Banach space; normalized M-basis; Orlicz-Pettis type result},

language = {eng},

number = {1},

pages = {65-80},

title = {A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces},

url = {http://eudml.org/doc/216460},

volume = {127},

year = {1998},

}

TY - JOUR

AU - Androulakis, G.

TI - A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces

JO - Studia Mathematica

PY - 1998

VL - 127

IS - 1

SP - 65

EP - 80

AB - 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.

LA - eng

KW - isomorphically polyhedral Banach space; normalized M-basis; Orlicz-Pettis type result

UR - http://eudml.org/doc/216460

ER -

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