{"paper":{"title":"Spectrum of $J$-frame operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alejandra Maestripieri, Carsten Trunk, Francisco Mart\\'inez Per\\'ia, Juan Ignacio Giribet, Leslie Leben, Matthias Langer","submitted_at":"2017-03-10T12:59:30Z","abstract_excerpt":"A $J$-frame is a frame $\\mathcal{F}$ for a Krein space $(\\mathcal{H}, [\\, , \\,])$ which is compatible with the indefinite inner product $[\\, , \\, ]$ in the sense that it induces an indefinite reconstruction formula that resembles those produced by orthonormal bases in $\\mathcal{H}$. With every $J$-frame the so-called $J$-frame operator is associated, which is a self-adjoint operator in the Krein space $\\mathcal{H}$. The $J$-frame operator plays an essential role in the indefinite reconstruction formula.\n  In this paper we characterize the class of $J$-frame operators in a Krein space by a $2\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03665","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"}