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arxiv: 1512.07776 · v2 · pith:TXANQMSRnew · submitted 2015-12-24 · 🧮 math.OA

Crossed products of operator spaces

classification 🧮 math.OA
keywords operatorcrossedspacealgebraalphagroupproductbijective
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Let $V$ be an operator space and $\iso(V)$ be the group of all completely isometric bijective linear mappings on $V$. Let $G$ act on $V$ via a strongly continuous group homomorphism $\alpha:G \to \iso (V)$. We define the full (and reduced) operator space crossed product $V\rtimes^{\op}_{\alpha,(r)}G$ and show that for a $C^*$-algebra with its canonical operator space structure, it coincides with the corresponding $C^*$-algebra crossed product. Unfortunately, the proof of Theorem 4.3 of the paper contains a serious gap, which leads to the withdrawal of the paper.

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