{"paper":{"title":"Frames of subspaces in Hilbert spaces with $W$-metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Kevin Esmeral, Osmin Ferrer, Primitivo Acosta-Hum\\'anez","submitted_at":"2013-09-05T01:46:58Z","abstract_excerpt":"If $\\left(\\h,\\langle\\cdot,\\cdot\\rangle\\right)$ is a Hilbert space and on it we consider the sesquilinear form $\\langle\\,W\\cdot,\\cdot\\rangle$ so-called $W$-metric, where $W^{*}=W\\in\\BH$, and $\\ker\\,W=\\{0\\}$, then the space $\\left(\\h,\\langle\\,W\\cdot,\\cdot\\rangle\\right)$ is called Hilbert space with $W$-metric or simply $W$-space. In this paper we investigate the dynamic of frames of subspace on these spaces, where the sense of dynamics refers to the behavior of frames of subspace in $\\h_{W}$ (the completion of $\\left(\\h,\\langle\\,W\\cdot,\\cdot\\rangle\\right)$) comparing with $\\h$ and vice versa. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1219","kind":"arxiv","version":2},"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"}