Journal of Convex Analysis 06 (1999), No. 1, 183--194
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 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.
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