{"paper":{"title":"Invertible completions of FLI and FRI upper triangular operator matrices","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Nikola Sarajlija","submitted_at":"2025-08-28T16:18:14Z","abstract_excerpt":"If $A\\in\\mathcal{B}(\\mathcal{H})$ and $B\\in\\mathcal{B}(\\mathcal{K})$ are given operators, denote by $M_C$ an operator matrix of the form $$M_C=\\begin{pmatrix}\n  A & C\\\\ 0 & B \\end{pmatrix}\\in\\mathcal{B}(\\mathcal{H}\\oplus\\mathcal{K})$$ acting on a direct sum of infinite dimensional separable Hilbert spaces $\\mathcal{H}$ and $\\mathcal{K}$, where $C\\in\\mathcal{B}(\\mathcal{K},\\mathcal{H})$ is unknown. In this article we solve the completion problem of $M_C$ to Fredholm left and Fredholm right invertibility, and we obtain appropriate perturbation results as consequences. We illustrate our results b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.20956","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.20956/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"}