
Journal of Convex Analysis 06 (1999), No. 1, 183194 Copyright Heldermann Verlag 1999 Denting Points in Bochner Banach Ideal Spaces X(E) H. Benabdellah Dép. de Mathématiques, Faculté des Sciences, Semlalia, B.P. S15, Marrakech, Marocco Let (X, ._{X}) be an ordercontinuous Banach ideal space over a σfinite 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. [ Fulltextpdf (216 KB)] 