Geodesic
An alternative proof of Diestel's theorem
Glasgow mathematical journal, Tome 25 (1984) no. 1, pp. 45-46

Voir la notice de l'article provenant de la source Cambridge University Press

We show that Diestel's theorem on weak compactness of subsets of L1,(μ, X) can be derived as a simple corollary of James's theorem. It is a pleasure to acknowledge several stimulating conserversations with Dave Emmons and the remarks of an anonymous referee. Errors are, of course, solely mine. 
Khan, M. Ali. An alternative proof of Diestel's theorem. Glasgow mathematical journal, Tome 25 (1984) no. 1, pp. 45-46. doi: 10.1017/S0017089500005413
@article{10_1017_S0017089500005413,
     author = {Khan, M. Ali},
     title = {An alternative proof of {Diestel's} theorem},
     journal = {Glasgow mathematical journal},
     pages = {45--46},
     year = {1984},
     volume = {25},
     number = {1},
     doi = {10.1017/S0017089500005413},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500005413/}
}
TY  - JOUR
AU  - Khan, M. Ali
TI  - An alternative proof of Diestel's theorem
JO  - Glasgow mathematical journal
PY  - 1984
SP  - 45
EP  - 46
VL  - 25
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500005413/
DO  - 10.1017/S0017089500005413
ID  - 10_1017_S0017089500005413
ER  - 
%0 Journal Article
%A Khan, M. Ali
%T An alternative proof of Diestel's theorem
%J Glasgow mathematical journal
%D 1984
%P 45-46
%V 25
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500005413/
%R 10.1017/S0017089500005413
%F 10_1017_S0017089500005413

[1] 1.Brooks, J. K., Equicontinuous sets of measures and applications to Vitali's integral convergence theorem and control measures, Advances in Math. 10 (1973), 165–171. Google Scholar | DOI

[2] 2.Davis, W. J., Figiel, T., Johnson, W. B. and Pelczynski, A., Factoring weakly compact operators, J. Functional Analysis 17 (1974), 311–327. Google Scholar | DOI

[3] 3.Diestel, J., Remarks on weak compactness in L,(μ, X), Glasgow Math. J. 18 (1977), 87–91. Google Scholar | DOI

[4] 4.Diestel, J. and Uhl, J. J. Jr, Vector measures, American Mathematical Society (Providence, Rhode Island, 1977). Google Scholar | DOI

[5] 5.James, R. C., Weakly compact sets, Trans. Amer. Math. Soc. 113 (1964), 129–140. Google Scholar | DOI

Cité par Sources :