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

@article{AIF_1976__26_2_25_0,
     author = {Wickstead, A. W.},
     title = {A characterization of weakly sequentially complete Banach lattices},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {26},
     number = {2},
     year = {1976},
     pages = {25-28},
     doi = {10.5802/aif.611},
     zbl = {0295.46017},
     mrnumber = {53 \#14080},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1976__26_2_25_0}
}
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. http://www.numdam.org/item/AIF_1976__26_2_25_0/

[1] J. P. R. Christensen, Borel structures in groups and semi-groups, Math. Scand., 28 (1971) 124-128. | MR 46 #7436 | Zbl 0217.08502

[2] J. P. R. Christensen, Borel structures and a topological zero-one law, Math. Scand., 29 (1971), 245-255. | MR 47 #2021 | Zbl 0234.54024

[3] D. H. Fremlin, Abstract Kothe spaces II, Proc. Cam. Phil. Soc., 63 (1967), 951-956. | MR 35 #7107 | Zbl 0179.17005

[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 0147.11001

[5] P. Meyer-Nieberg, Zur schwachen Kompaktheit in Banachverbanden, Math. Z.j 134 (1973), 303-315. | MR 48 #9341 | Zbl 0268.46010