Denting Points in Bochner Banach Ideal Spaces X(E)

Let

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 \longmapsto \|f(t)\| ∣ f ∣ : t ⟼ ∥ f ( t ) ∥

is a denting point of the unit ball of X and (ii)

f(t)/\|f(t)\| 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