{"paper":{"title":"Multiplicative Lidskii's inequalities and optimal perturbations of frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Demetrio Stojanoff, Mariano A. Ruiz, Pedro G. Massey","submitted_at":"2014-05-16T19:29:12Z","abstract_excerpt":"In this paper we study two design problems in frame theory: on the one hand, given a fixed finite frame $\\cF$ for $\\hil\\cong\\C^d$ we compute those dual frames $\\cG$ of $\\cF$ that are optimal perturbations of the canonical dual frame for $\\cF$ under certain restrictions on the norms of the elements of $\\cG$. On the other hand, for a fixed finite frame $\\cF=\\{f_j\\}_{j\\in\\In}$ for $\\hil$ we compute those invertible operators $V$ such that $V^*V$ is a perturbation of the identity and such that the frame $V\\cdot \\cF=\\{V\\,f_j\\}_{j\\in\\In}$ - which is equivalent to $\\cF$ - is optimal among such pertur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4277","kind":"arxiv","version":1},"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"}