Geodesic
Denting Points in Bochner Banach Ideal Spaces X(E)
Journal of convex analysis, Tome 6 (1999) no. 1, pp. 183-194

Voir la notice de l'article provenant de la source Heldermann Verlag

Let (X, ||.||X) be an order-continuous Banach ideal space over a σ-finite measure space (Ω, Σ, μ) and E a Banach space. We prove that a function f of the vector Banach ideal space X(E) is a denting point of the unit ball of X(E) if and only if: (i) the modulus function |f|: t ---> ||f(t)|| is a denting point of the unit ball of X and (ii) f(t) / ||f(t)|| is a denting point of the unit ball of E for almost all t in supp(f). This gives an answer to the open problem raised in a paper of Castaing and Pluciennik. 
@article{JCA_1999_6_1_JCA_1999_6_1_a10,
     author = {H. Benabdellah},
     title = {Denting {Points} in {Bochner} {Banach} {Ideal} {Spaces} {X(E)}},
     journal = {Journal of convex analysis},
     pages = {183--194},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {1999},
     url = {http://geodesic.mathdoc.fr/item/JCA_1999_6_1_JCA_1999_6_1_a10/}
}
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H. Benabdellah. Denting Points in Bochner Banach Ideal Spaces X(E). Journal of convex analysis, Tome 6 (1999) no. 1, pp. 183-194. http://geodesic.mathdoc.fr/item/JCA_1999_6_1_JCA_1999_6_1_a10/