{"paper":{"title":"$^{*}$-Regularity of Operator Space Projective Tensor Product of C$^{*}$-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ajay Kumar, Vandana Rajpal","submitted_at":"2011-12-02T12:25:04Z","abstract_excerpt":"The Banach $^{*}$-algebra $A\\hat{\\otimes}B$, the operator space projective tensor product of $C^{*}$-algebras $A$ and $B$, is shown to be $^{*}$-regular if Tomiyama's property ($F$) holds for $A\\otimes_{\\min}B$ and $A \\otimes_{\\min}B=A \\otimes_{\\max}B$, where $\\otimes_{\\min}$ and $\\otimes_{\\max}$ are the injective and projective $C^{*}$-cross norm, respectively. However, $A\\hat{\\otimes}B$ has a unique $C^{*}$-norm if and only if $A\\otimes B$ has. We also discuss the property ($F$) of $A\\hat{\\otimes}B$ and $A\\otimes_{h}B$, the Haagerup tensor product of $A$ and $B$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0444","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"}