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On operator systems generated by reducible projective unitary representations of compact groups. (English) Zbl 07164313

Summary: We study reducible projective unitary representations \((U_g)_{g\in G}\) of a compact group \(G\) in separable Hilbert spaces \(H\). It is shown that there exist the projections \(Q\) and \(P\) for which \(\mathcal{V}=\overline{span(U_gQU_g^*, g\in G)}\) is the operator system and \(P\mathcal{V}P=\{\mathbb{C}P\}\). As an example, a bipartite Hilbert space \(H=\mathfrak{H}\otimes\mathfrak{H}\) is considered. In this case, the action of \((U_g)_{g\in G}\) has the property of transforming separable vectors to entangled.

MSC:

47L05 Linear spaces of operators
22D10 Unitary representations of locally compact groups
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References:

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