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Turkish Journal of Mathematics

Authors

GRIGORI AMOSOV

DOI

10.3906/mat-1906-59

Abstract

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.

First Page

2366

Last Page

2370

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Mathematics Commons

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