{"paper":{"title":"Operator convexity in Krein spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"M. Dehghani, M. S. Moslehian","submitted_at":"2014-01-14T16:07:14Z","abstract_excerpt":"We introduce the notion of Krein-operator convexity in the setting of Krein spaces. We present an indefinite version of the Jensen operator inequality on Krein spaces by showing that if $(\\mathscr{H},J)$ is a Krein space, $\\mathcal{U}$ is an open set which is symmetric with respect to the real axis such that $\\mathcal{U}\\cap\\mathbb{R}$ consists of a segment of real axis and $f$ is a Krein-operator convex function on $\\mathcal{U}$ with $f(0)=0$, then \\begin{eqnarray*} f(C^{\\sharp}AC)\\leq^{J}C^{\\sharp}f(A)C \\end{eqnarray*} for all $J$-positive operators $A$ and all invertible $J$-contractions $C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3238","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"}