- Turkish Journal of Mathematics
- Vol: 43 Issue: 5
- On operator systems generated by reducible projective unitary representations of compact groups
On operator systems generated by reducible projective unitary representations of compact groups
Authors : Grigori Amosov
Pages : 2366-2370
View : 9 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Operator systems, covariant resolutions of identity, reducible unitary representations of compact groups, quantum anticliques