{"paper":{"title":"Shift invariant preduals of $\\ell_1(\\Z)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Matthew Daws, Richard Haydon, Stuart White, Thomas Schlumprecht","submitted_at":"2011-01-29T14:35:04Z","abstract_excerpt":"The Banach space $\\ell_1(\\Z)$ admits many non-isomorphic preduals, for example, $C(K)$ for any compact countable space $K$, along with many more exotic Banach spaces. In this paper, we impose an extra condition: the predual must make the bilateral shift on $\\ell_1(\\Z)$ weak$^*$-continuous. This is equivalent to making the natural convolution multiplication on $\\ell_1(\\Z)$ separately weak*-continuous and so turning $\\ell_1(\\Z)$ into a dual Banach algebra. We call such preduals \\emph{shift-invariant}. It is known that the only shift-invariant predual arising from the standard duality between $C_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5696","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":""},"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"}