{"paper":{"title":"Some Operator Bounds Employing Complex Interpolation Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.FA","authors_text":"Fedor Sukochev, Fritz Gesztesy, Yuri Latushkin, Yuri Tomilov","submitted_at":"2014-05-07T06:45:15Z","abstract_excerpt":"We revisit and extend known bounds on operator-valued functions of the type $$ T_1^{-z} S T_2^{-1+z}, \\quad z \\in \\ol \\Sigma = \\{z\\in\\bbC\\,|\\, \\Re(z) \\in [0,1]\\}, $$ under various hypotheses on the linear operators $S$ and $T_j$, $j=1,2$. We particularly single out the case of self-adjoint and sectorial operators $T_j$ in some separable complex Hilbert space $\\cH_j$, $j=1,2$, and suppose that $S$ (resp., $S^*$) is a densely defined closed operator mapping $\\dom(S) \\subseteq \\cH_1$ into $\\cH_2$ (resp., $\\dom(S^*) \\subseteq \\cH_2$ into $\\cH_1$), relatively bounded with respect to $T_1$ (resp., $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1517","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"}