{"paper":{"title":"On the binary relation $\\leq_u$ on self-adjoint Hilbert space operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"H. Najafi, M. S. Moslehian, S. M. S. Nabavi Sales","submitted_at":"2012-04-10T17:12:24Z","abstract_excerpt":"Given self-adjoint operators $A, B\\in\\mathbb{B}(\\mathscr{H})$ it is said $A\\leq_uB$ whenever $A\\leq U^*BU$ for some unitary operator $U$. We show that $A\\leq_u B$ if and only if $f(g(A)^r)\\leq_uf(g(B)^r)$ for any increasing operator convex function $f$, any operator monotone function $g$ and any positive number $r$. We present some sufficient conditions under which if $B\\leq A\\leq U^*BU$, then $B=A=U^*BU$. Finally we prove that if $A^n\\leq U^\\ast A^nU$ for all $n\\in\\mathbb{N}$, then $A=U^\\ast AU$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2222","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"}