Some remarks on $M$-ideals and strong proximinality
Bull. Korean Math. Soc. 2003 Vol. 40, No. 3, 503-508
Published online September 1, 2003
Catherine Finet and Lucas Quarta
Universite de Mons-Hainaut, Universite de Mons-Hainaut
Abstract : We prove that every $M$-ideal is strongly proximinal and that, for any Banach space $X$, $K(X,c_0)$ is an $M$-ideal in $L(X,\ell^\infty)$.
Keywords : proximinality, $M$-ideals, $n$-ball property, $1 \frac 12$-ball property, compact operators
MSC numbers : 41A50, 41A65, 46B20
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