A note on Dunford-Pettis operators
Glasgow mathematical journal, Tome 29 (1987) no. 2, pp. 271-273
Voir la notice de l'article provenant de la source Cambridge University Press
Talagrand has shown [4, p. 76] that there exists a continuous linear operator from L1[0, 1] to c0 which is not a Dunford-Pettis operator. In contrast to this result, Gretsky and Ostroy [2] have recently proved that every positive operator from L[0, 1] to c0 is a Dunford-Pettis operator, hence that every regular operator between these spaces (i.e. a difference of positive operators) is Dunford-Pettis.
Holub, J. R. A note on Dunford-Pettis operators. Glasgow mathematical journal, Tome 29 (1987) no. 2, pp. 271-273. doi: 10.1017/S0017089500006935
@article{10_1017_S0017089500006935,
author = {Holub, J. R.},
title = {A note on {Dunford-Pettis} operators},
journal = {Glasgow mathematical journal},
pages = {271--273},
year = {1987},
volume = {29},
number = {2},
doi = {10.1017/S0017089500006935},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500006935/}
}
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[2] 2. Gretsky, N. and Ostroy, J., The compact range property and c , Glasgow Math. J. 28 (1986), 113–114. Google Scholar | DOI
[3] 3. Schaefer, H., Topological vector spaces (Macmillan, 1966). Google Scholar
[4] 4. Talagrand, M., Pettis integral and measure theory, Mem. Amer. Math. Soc. 307 (1984). Google Scholar
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