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

Nigel J. Kalton; Dirk Werner

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

Functional Analysis 2008-02-03 v1

Authors: Nigel J. Kalton , Dirk Werner

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.

Keywords

M-ideals bounded linear operators L(L_p) K(l_p(l_q^n)) conjecture

Cite

@article{arxiv.math/9308206,
  title  = {The $M$-ideal structure of some algebras of bounded linear operators},
  author = {Nigel J. Kalton and Dirk Werner},
  journal= {arXiv preprint arXiv:math/9308206},
  year   = {2008}
}

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