Geodesic
$M$-ideals of compact operators into $\ell_p$
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 1, pp. 51-57

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We show for $2\le p\infty $ and subspaces $X$ of quotients of $L_{p}$ with a $1$-unconditional finite-dimensional Schauder decomposition that $K(X,\ell _{p})$ is an $M$-ideal in $L(X,\ell _{p})$.
Classification : 46B28, 47B07, 47L05 
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     author = {John, Kamil and Werner, Dirk},
     title = {$M$-ideals of compact operators into $\ell_p$},
     journal = {Czechoslovak Mathematical Journal},
     pages = {51--57},
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     zbl = {1040.46020},
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John, Kamil; Werner, Dirk. $M$-ideals of compact operators into $\ell_p$. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 1, pp. 51-57. http://geodesic.mathdoc.fr/item/CMJ_2000__50_1_a6/