{"paper":{"title":"Stability of low-rank matrix recovery and its connections to Banach space geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.FA","authors_text":"Denka Kutzarova, Javier Alejandro Ch\\'avez-Dom\\'inguez","submitted_at":"2014-06-25T20:36:44Z","abstract_excerpt":"There are well-known relationships between compressed sensing and the geometry of the finite-dimensional $\\ell_p$ spaces. A result of Kashin and Temlyakov can be described as a characterization of the stability of the recovery of sparse vectors via $\\ell_1$-minimization in terms of the Gelfand widths of certain identity mappings between finite-dimensional $\\ell_1$ and $\\ell_2$ spaces, whereas a more recent result of Foucart, Pajor, Rauhut and Ullrich proves an analogous relationship even for $\\ell_p$ spaces with $p < 1$. In this paper we prove what we call matrix or noncommutative versions of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6712","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}