Geometry of Banach spaces and biorthogonal systems

S. Dilworth; Maria Girardi; W. Johnson

Studia Mathematica (2000)

  • Volume: 140, Issue: 3, page 243-271
  • ISSN: 0039-3223

Abstract

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A separable Banach space X contains 1 isomorphically if and only if X has a bounded fundamental total w c 0 * -stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded fundamental total w c 0 * -biorthogonal system.

How to cite

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Dilworth, S., Girardi, Maria, and Johnson, W.. "Geometry of Banach spaces and biorthogonal systems." Studia Mathematica 140.3 (2000): 243-271. <http://eudml.org/doc/216766>.

@article{Dilworth2000,
abstract = {A separable Banach space X contains $ℓ_1$ isomorphically if and only if X has a bounded fundamental total $wc_\{0\}*$-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded fundamental total $wc_\{0\}*$-biorthogonal system.},
author = {Dilworth, S., Girardi, Maria, Johnson, W.},
journal = {Studia Mathematica},
keywords = {geometric properties of a Banach space; bounded fundamental total biorthogonal system; Schur property},
language = {eng},
number = {3},
pages = {243-271},
title = {Geometry of Banach spaces and biorthogonal systems},
url = {http://eudml.org/doc/216766},
volume = {140},
year = {2000},
}

TY - JOUR
AU - Dilworth, S.
AU - Girardi, Maria
AU - Johnson, W.
TI - Geometry of Banach spaces and biorthogonal systems
JO - Studia Mathematica
PY - 2000
VL - 140
IS - 3
SP - 243
EP - 271
AB - A separable Banach space X contains $ℓ_1$ isomorphically if and only if X has a bounded fundamental total $wc_{0}*$-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded fundamental total $wc_{0}*$-biorthogonal system.
LA - eng
KW - geometric properties of a Banach space; bounded fundamental total biorthogonal system; Schur property
UR - http://eudml.org/doc/216766
ER -

References

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