{"paper":{"title":"Surjective homomorphisms from algebras of operators on long sequence spaces are automatically injective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Bence Horv\\'ath, Tomasz Kania","submitted_at":"2020-07-28T10:34:55Z","abstract_excerpt":"We study automatic injectivity of surjective algebra homomorphisms from $\\mathscr{B}(X)$, the algebra of (bounded, linear) operators on $X$, to $\\mathscr{B}(Y)$, where $X$ is one of the following \\emph{long} sequence spaces: $c_0(\\lambda)$, $\\ell_{\\infty}^c(\\lambda)$, and $\\ell_p(\\lambda)$ ($1 \\leqslant p < \\infty$) and $Y$ is arbitrary. \\textit{En route} to the proof that these spaces do indeed enjoy such a property, we classify two-sided ideals of the algebra of operators of any of the aforementioned Banach spaces that are closed with respect to the `sequential strong operator topology'."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.14112","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/2007.14112/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"}