{"paper":{"title":"Generalized frame operator distance problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Demetrio Stojanoff, Noelia Rios, Pedro Massey","submitted_at":"2018-12-26T16:37:51Z","abstract_excerpt":"Let $S\\in\\mathcal{M}_d(\\mathbb{C})^+$ be a positive semidefinite $d\\times d$ complex matrix and let $\\mathbf a=(a_i)_{i\\in\\mathbb{I}_k}\\in \\mathbb{R}_{>0}^k$, indexed by $\\mathbb{I}_k=\\{1,\\ldots,k\\}$, be a $k$-tuple of positive numbers. Let $\\mathbb T_{d}(\\mathbf a )$ denote the set of families $\\mathcal G=\\{g_i\\}_{i\\in\\mathbb{I}_k}\\in (\\mathbb{C}^d)^k$ such that $\\|g_i\\|^2=a_i$, for $i\\in\\mathbb{I}_k$; thus, $\\mathbb T_{d}(\\mathbf a )$ is the product of spheres in $\\mathbb{C}^d$ endowed with the product metric. For a strictly convex unitarily invariant norm $N$ in $\\mathcal{M}_d(\\mathbb{C})$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10365","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"}