On operator systems generated by reducible projective unitary representations of compact groups

Abstract

We study reducible projective unitary representations ${(U_g)}_{gin G}$ of a compact group G in separable Hilbertspaces H. It is shown that there exist the projections Q and P for which $V=overline{spa{(U_gQU_g,;gin G)}_;};;$ is the operatorsystem and $PVP={mathbb{C}P}$. As an example, a bipartite Hilbert space H = H ⊗ H is considered. In this case, the actionof ${(U_g)}_{gin G}$