{"paper":{"title":"Relatively bounded operators and the operator E-norms (addition to arXiv:1806.05668)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OA","quant-ph"],"primary_cat":"math.FA","authors_text":"M.E.Shirokov","submitted_at":"2018-11-23T20:16:22Z","abstract_excerpt":"In this brief note we describe relations between the well known notion of a relatively bounded operator and the operator E-norms considered in [arXiv:1806.05668].\n  We show that the set of all $\\sqrt{G}$-bounded operators equipped with the E-norm induced by a positive operator $G$ is the Banach space of all operators with finite E-norm and that the $\\sqrt{G}$-bound is a continuous seminorm on this space.\n  We also show that the set of all $\\sqrt{G}$-infinitesimal operators (operators with zero $\\sqrt{G}$-bound) equipped with the E-norm induced by a positive operator $G$ is the completion of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09659","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"}