Dep. de Mathematiques, Faculte des Sciences, Semlalia, B.P : S15, Marrakech, Marocco, benabdellah@ucam.ac.ma
Abstract: Let $(X, \|.\|_{X})$ be an order-continuous Banach ideal space over a $\sigma-$ finite measure space $(\Omega,\Sigma,\mu)$ 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 $|f| : t\longmapsto \|f(t)\|$ 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 the paper [3].
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