{"paper":{"title":"W^*-derived sets of transfinite order of subspaces of dual Banach spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mikhail I. Ostrovskii","submitted_at":"1993-03-29T17:51:57Z","abstract_excerpt":"It is an English translation of the paper originally published in Russian and Ukrainian in 1987. In the appendix of his book S.Banach introduced the following definition Let $X$ be a Banach space and $\\Gamma$ be a subspace of the dual space $X^*$. The set of all limits of $w^{*}$-convergent sequences in $\\Gamma $ is called the $w^*${\\it -derived set} of $\\Gamma $ and is denoted by $\\Gamma _{(1)}$. For an ordinal $\\alpha$ the $w^{*}$-{\\it derived set of order} $\\alpha $ is defined inductively by the equality: $$ \\Gamma _{(\\alpha )}=\\bigcup _{\\beta <\\alpha }((\\Gamma _{(\\beta )})_{(1)}. $$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9303203","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"}