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The $M$-ideal structure of some algebras of bounded linear operators

Nigel J. Kalton·Dirk Werner
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Abstract

Let $1<p,\,q<\infty$. It is shown for complex scalars that there are no nontrivial $M$-ideals in $L(L_p[0,1])$ if $p\neq 2$, and $K(\ell_p(\ell_q^n)$ is the only nontrivial $M$-ideal in $L(\ell_p(\ell_q^n)$. This proves a conjecture of C.-M. Cho and W. B. Johnson.

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Nigel J. Kalton, Dirk Werner. 1993-08-13. The $M$-ideal structure of some algebras of bounded linear operators. https://arxiv.org/abs/math/9308206

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