{"paper":{"title":"Hyperinvariant subspaces of hyponormal operators: A constructive decomposition approach","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Eva A. Gallardo-Guti\\'errez, Norberto Clemente","submitted_at":"2026-05-30T19:40:40Z","abstract_excerpt":"It is shown that any hyponormal operator on an infinite-dimensional separable Hilbert space that admits a decomposition \\( T = R + V \\), where \\( R \\) is tridiagonal and \\( V \\) is trace-class, has nontrivial closed hyperinvariant subspaces provided $T$ is not a multiple of the identity. We further discuss implications of this result for the invariant subspace problem of hyponormal operators answering, in particular, negatively to a question raised by Kim and Lee \\cite{kimlee} regarding an explicit approach to such a problem. Finally, we characterize the existence of reducing subspaces for hyp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00865","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/2606.00865/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"}