{"paper":{"title":"A Kadec-Pelczy\\'nski dichotomy-type theorem for preduals of JBW*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Antonio M. Peralta, Francisco J. Fern\\'andez-Polo, Mar\\'Ia Isabel Ram\\'Irez","submitted_at":"2012-11-21T10:48:02Z","abstract_excerpt":"We prove a Kadec-Pelczy\\'nski dichotomy-type theorem for bounded sequences in the predual of a JBW*-algebra, showing that for each bounded sequence $(\\phi_n)$ in the predual of a JBW$^*$-algebra $M$, there exist a subsequence $(\\phi_{\\tau(n)})$, and a sequence of mutually orthogonal projections $(p_n)$ in $M$ such that: [$(a)$] the set ${\\phi_{\\tau(n)} - \\phi_{\\tau(n)} P_{2} (p_n): n\\in \\mathbb{N}}$ is relatively weakly compact, $\\phi_{\\tau(n)}=\\xi_n+\\psi_n$, with $\\xi_n := \\phi_{\\tau(n)} - \\phi_{\\tau(n)} P_{2} (p_n)$, and $\\psi_n := \\phi_{\\tau(n)} P_{2} (p_n),$ {\\rm(}$\\xi_n Q(p_n)= 0$ and $\\p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4990","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"}