{"paper":{"title":"Structure of total subspaces of dual Banach spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mikhail I. Ostrovskii","submitted_at":"1993-10-26T15:12:34Z","abstract_excerpt":"Let $X$ be a separable nonquasireflexive Banach space. Let $Y$ be a Banach space isomorphic to a subspace of $X^*$. The paper is devoted to the following questions: 1. Under what conditions does there exist an isomorphic embedding $T:Y\\to X^*$ such that subspace $T(Y)\\subset X^*$ is total? 2. If such embeddings exist, what are the possible orders of $T(Y)$?\n  Here we need to recall some definitions. For a subset $M\\subset X^*$ we denote the set of all limits of weak$^*$ convergent sequences in $M$ by $M_{(1)}$. Inductively, for ordinal number $\\alpha$ we let $$M_{(\\alpha)}=\\cup_{\\beta<\\alpha}("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9310218","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"}