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

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.

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.

@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},
     pages = {25--28},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {26},
     number = {2},
     year = {1976},
     doi = {10.5802/aif.611},
     zbl = {0295.46017},
     mrnumber = {53 #14080},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.611/}
}
TY  - JOUR
AU  - Wickstead, A. W.
TI  - A characterization of weakly sequentially complete Banach lattices
JO  - Annales de l'Institut Fourier
PY  - 1976
SP  - 25
EP  - 28
VL  - 26
IS  - 2
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.611/
DO  - 10.5802/aif.611
LA  - en
ID  - AIF_1976__26_2_25_0
ER  - 
%0 Journal Article
%A Wickstead, A. W.
%T A characterization of weakly sequentially complete Banach lattices
%J Annales de l'Institut Fourier
%D 1976
%P 25-28
%V 26
%N 2
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.611/
%R 10.5802/aif.611
%G en
%F AIF_1976__26_2_25_0
Wickstead, A. W. A characterization of weakly sequentially complete Banach lattices. Annales de l'Institut Fourier, Tome 26 (1976) no. 2, pp. 25-28. doi : 10.5802/aif.611. https://aif.centre-mersenne.org/articles/10.5802/aif.611/

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

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

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

[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

Cité par Sources :