Some remarks on $M$-ideals and strong proximinality

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Bull. Korean Math. Soc. 2003; 40(3): 503-508

Printed September 1, 2003

Catherine Finet and Lucas Quarta

Universite de Mons-Hainaut, Universite de Mons-Hainaut

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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