{"paper":{"title":"A characterization of reflexive spaces of operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Janko Bra\\v{c}i\\v{c}, Lina Oliveira","submitted_at":"2015-11-25T10:58:18Z","abstract_excerpt":"We show that for a linear space of operators ${\\mathcal M}\\subseteq {\\mathcal B}(H_1,H_2)$ the following assertions are equivalent.\n  (i) ${\\mathcal M} $ is reflexive in the sense of Loginov--Shulman. (ii) There exists an order-preserving map $\\Psi=(\\psi_1,\\psi_2)$ on a bilattice\n  $Bil({\\mathcal M})$ of subspaces determined by ${\\mathcal M}$, with $P\\leq \\psi_1(P,Q)$ and $Q\\leq \\psi_2(P,Q)$, for any pair $(P,Q)\\in Bil({\\mathcal M})$, and\n  such that an operator $T\\in {\\mathcal B}(H_1,H_2)$ lies in ${\\mathcal M}$ if and only if $\\psi_2(P,Q)T\\psi_1(P,Q)=0$ for all\n  $(P,Q)\\in Bil( {\\mathcal M})"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08014","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"}