{"paper":{"title":"The closure of two-sided multiplications on C*-algebras and phantom line bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ilja Gogi\\'c, Richard M. Timoney","submitted_at":"2016-01-25T23:28:35Z","abstract_excerpt":"For a C*-algebra A we consider the problem of when the set $TM_0(A)$ of all two-sided multiplications $x \\mapsto axb$ ($a,b \\in A$) on A is norm closed, as a subset of B(A). We first show that $TM_0(A)$ is norm closed for all prime C*-algebras A. On the other hand, if $A\\cong \\Gamma_0(E )$ is an n-homogeneous C*-algebra, where E is the canonical $\\mathbb{M}_n $-bundle over the primitive spectrum X of A, we show that $TM_0(A)$ fails to be norm closed if and only if there exists a $\\sigma$-compact open subset U of X and a phantom complex line subbundle L of E over U (i.e. L is not globally trivi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06848","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"}