no. 2
A characterization of weakly sequentially complete Banach lattices
Annales de l'Institut Fourier, Volume 26 (1976) no. 2, pp. 25-28.

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.

On montre que pour tout espace de Banach E réticulé, les deux propriétés suivantes sont équivalentes :

1) E est faiblement séquentiellement complet.

2) Toute forme linéaire σ(E ′ ,E)-mesurable sur le dual topologique E ′ est continue.

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     author = {Wickstead, A. W.},
     title = {A characterization of weakly sequentially complete {Banach} lattices},
     journal = {Annales de l'Institut Fourier},
     pages = {25--28},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {26},
     number = {2},
     year = {1976},
     doi = {10.5802/aif.611},
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     mrnumber = {53 #14080},
     language = {en},
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Wickstead, A. W. A characterization of weakly sequentially complete Banach lattices. Annales de l'Institut Fourier, Volume 26 (1976) no. 2, pp. 25-28. doi : 10.5802/aif.611. https://aif.centre-mersenne.org/articles/10.5802/aif.611/

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[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. | Zbl

[5] P. Meyer-Nieberg, Zur schwachen Kompaktheit in Banachverbanden, Math. Z.j 134 (1973), 303-315. | MR | Zbl

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