The equivalence of the two following properties is proved for every Banach lattice :
1) is weakly sequentially complete.
2) Every -Borel measurable linear functional on is -continuous.
On montre que pour tout espace de Banach réticulé, les deux propriétés suivantes sont équivalentes :
1) est faiblement séquentiellement complet.
2) Toute forme linéaire -mesurable sur le dual topologique 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}, 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/ UR - https://zbmath.org/?q=an%3A0295.46017 UR - https://www.ams.org/mathscinet-getitem?mr=53 #14080 UR - https://doi.org/10.5802/aif.611 DO - 10.5802/aif.611 LA - en ID - AIF_1976__26_2_25_0 ER -
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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