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

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 $p\ne 2$, 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.

Cited by in corpus (1)

• Property $(M)$, $M$-ideals, and almost isometric structure of Banach spaces