Geodesic
The compact range property and C0
Glasgow mathematical journal, Tome 28 (1986) no. 1, pp. 113-114

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

The purpose of this short note is to make an observation about Dunford–Pettis operators from L1[0, 1] to C0. Recall that an operator T:E→F (where E and F are Banach spaces) is called Dunford–Pettis if T takes weakly convergent sequences of E into norm convergent sequences of F. A Banach space F has the Compact Range Property (CRP) if every operator T:L1]0, 1]→F is Dunford–Pettis. Talagrand shows in his book [2] that C0 does not have the CRP. It is of interest (especially in mathematical economics [3]) to note that every positive operator from L1[0, 1] to C0 is Dunford–Pettis. 
Gretsky, Neil E.; Ostroy, Joseph M. The compact range property and C0. Glasgow mathematical journal, Tome 28 (1986) no. 1, pp. 113-114. doi: 10.1017/S0017089500006406
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[1] 1.Bourgain, J., Dunford–Pettis operator on L1 and the Radon–Nikodyn property, Israel J. Math. 37 (1980), 34–27. Google Scholar | DOI

[2] 2.Talagrand, M., The Pettis integral, Mem. Amer. Math. Soc. No. 307, (Rhode Island, 1984). Google Scholar

[3] 3.Gretsky, N. E. and Ostroy, J. M., Thick and thin market non-atomic exchange economies, in Advances in Equilibrium Theory, Lecture Notes in Economics and Mathematical Systems No. 244 (1985), 107–130. Google Scholar | DOI

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