{"paper":{"title":"V*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Andre Kornell","submitted_at":"2015-02-05T12:23:45Z","abstract_excerpt":"What is the correct noncommutative generalization of the functor $C_0(X) \\mapsto \\ell^\\infty(X)$ for locally compact Hausdorff $X$ having a countable basis? Making the ansatz $K(\\ell^2) \\mapsto B(\\ell^2)$, we expect that every unital $*$-homomorphism $C(\\mathbb T) \\rightarrow B(\\ell^2)$ extend canonically to a unital $*$-homomorphism $\\ell^\\infty(\\mathbb T) \\rightarrow B(\\ell^2)$. Thus, we expect to extend the continuous functional calculus for a unitary operator on $\\ell^2$ to all bounded complex-valued functions.\n  Therefore, we work in a model of set theory where every set of real numbers i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01516","kind":"arxiv","version":3},"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"}