A characterization of weakly sequentially complete Banach lattices

A. W. Wickstead

Annales de l'institut Fourier (1976)

  • Volume: 26, Issue: 2, page 25-28
  • ISSN: 0373-0956

Abstract

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The equivalence of the two following properties is proved for every Banach lattice E :1) E is weakly sequentially complete.2) Every σ ( E * , E ) -Borel measurable linear functional on E is σ ( E * , E ) -continuous.

How to cite

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Wickstead, A. W.. "A characterization of weakly sequentially complete Banach lattices." Annales de l'institut Fourier 26.2 (1976): 25-28. <http://eudml.org/doc/74281>.

@article{Wickstead1976,
abstract = {The equivalence of the two following properties is proved for every Banach lattice $E$:1) $E$ is weakly sequentially complete.2) Every $\sigma (E^*,E)$-Borel measurable linear functional on $E$ is $\sigma (E^*,E)$-continuous.},
author = {Wickstead, A. W.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {25-28},
publisher = {Association des Annales de l'Institut Fourier},
title = {A characterization of weakly sequentially complete Banach lattices},
url = {http://eudml.org/doc/74281},
volume = {26},
year = {1976},
}

TY - JOUR
AU - Wickstead, A. W.
TI - A characterization of weakly sequentially complete Banach lattices
JO - Annales de l'institut Fourier
PY - 1976
PB - Association des Annales de l'Institut Fourier
VL - 26
IS - 2
SP - 25
EP - 28
AB - The equivalence of the two following properties is proved for every Banach lattice $E$:1) $E$ is weakly sequentially complete.2) Every $\sigma (E^*,E)$-Borel measurable linear functional on $E$ is $\sigma (E^*,E)$-continuous.
LA - eng
UR - http://eudml.org/doc/74281
ER -

References

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  1. [1] J. P. R. CHRISTENSEN, Borel structures in groups and semi-groups, Math. Scand., 28 (1971) 124-128. Zbl0217.08502MR46 #7436
  2. [2] J. P. R. CHRISTENSEN, Borel structures and a topological zero-one law, Math. Scand., 29 (1971), 245-255. Zbl0234.54024MR47 #2021
  3. [3] D. H. FREMLIN, Abstract Kothe spaces II, Proc. Cam. Phil. Soc., 63 (1967), 951-956. Zbl0179.17005MR35 #7107
  4. [4] W. A. LUXEMBURG and A. C. ZAANEN, Notes on Banach function spaces, Nederl. Akad. Wetensch. Proc. Ser. A., 67 (1964) (a) 507-518, (b) 519-529. Zbl0147.11001
  5. [5] P. MEYER-NIEBERG, Zur schwachen Kompaktheit in Banachverbanden, Math. Z.j 134 (1973), 303-315. Zbl0268.46010MR48 #9341

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