This is an announcement for the paper “Closed Ideals of Operators between the Classical Sequence Spaces” by Dan Freemanhttps://arxiv.org/find/math/1/au:+Freeman_D/0/1/0/all/0/1, Thomas Schlumprechthttps://arxiv.org/find/math/1/au:+Schlumprecht_T/0/1/0/all/0/1, Andras Zsakhttps://arxiv.org/find/math/1/au:+Zsak_A/0/1/0/all/0/1.

Abstract: We prove that the spaces $\mathcal{L}(\ell_p, c_0), \mathcal{L}(\ell_p, \ell_{\inty})$ and $\mathcal{L}(\ell_1, \ell_q)$ of operators with $1<p, q<\infty$ have continuum many closed ideals. This extends and improves earlier works by Schlumprecht and Zs'ak, by Wallis, and by Sirotkin and Wallis. Several open problems remain. Key to our construction of closed ideals are matrices with the Restricted Isometry Property that come from Compressed Sensing.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1612.01153