{"paper":{"title":"On the ascent and the angle between the null space and the range of elementary operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Bojan Kuzma, Hranislav Stankovi\\'c, Janko Bra\\v{c}i\\v{c}","submitted_at":"2026-06-17T11:05:24Z","abstract_excerpt":"We study the angle between the null space and the range of elementary operators of length one or two acting on $\\mathcal{B}(\\mathscr{X})$, the Banach algebra of all bounded linear operators on a complex Banach space $\\mathscr{X}$. For the multiplication operator $\\mu_{A,B}(X) = AXB$, we characterize positivity of this angle in terms of the corresponding angles for $A$ and $B^*$. For elementary operators of length two $\\Delta_{\\boldsymbol{A},\\boldsymbol{B}} = \\mu_{A_1,B_1} - \\mu_{A_2,B_2}$, we establish conditions under which the angle is positive, and the ascent of $\\Delta_{\\boldsymbol{A},\\bol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18930","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.18930/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}