Denting Points in Bochner Banach Ideal Spaces X(E)

H. Benabdellah

Journal of convex analysis, Tome 6 (1999) no. 1, pp. 183-194.

Résumé

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.