{"paper":{"title":"Upper triangular Toeplitz matrices and real parts of quasinilpotent operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Anna Skripka, Junsheng Fang, Ken Dykema","submitted_at":"2012-06-22T08:11:51Z","abstract_excerpt":"We show that every self--adjoint matrix B of trace 0 can be realized as B=T+T^* for a nilpotent matrix T of norm no greater than K times the norm of B, for a constant K that is independent of matrix size. More particularly, if D is a diagonal, self--adjoint n-by-n matrix of trace 0, then there is a unitary matrix V=XU_n, where X is an n-by-n permutation matrix and U_n is the n-by-n Fourier matrix, such that the upper triangular part, T, of the conjugate V^*DV of D has norm no greater than K times the norm of D. This matrix T is a strictly upper triangular Toeplitz matrix such that T+T^*=V^*DV."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5080","kind":"arxiv","version":3},"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"}