{"paper":{"title":"Admissible fundamental operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Haripada Sau, Sneh Lata, Tirthankar Bhattacharyya","submitted_at":"2014-04-23T13:32:37Z","abstract_excerpt":"Let $F$ and $G$ be two bounded operators on two Hilbert spaces. Let their numerical radii be no greater than one. This note investigate when there is a $\\Gamma$-contraction $(S,P)$ such that $F$ is the fundamental operator of $(S,P)$ and $G$ is the fundamental operator of $(S^*,P^*)$. Theorem 1 puts a necessary condition on $F$ and $G$ for them to be the fundamental operators of $(S,P)$ and $(S^*,P^*)$ respectively. Theorem 2 shows that this necessary condition is sufficient too provided we restrict our attention to a certain special case. The general case is investigated in Theorem 3. Some of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5819","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"}