On truncated t-free Fock spaces: Spectrum of position operators and shift-invariant states

The ergodic properties of the shift on the C*-algebras generated by creators and annihilators on both the full and m-truncated t-free Fock spaces are analyzed. In particular, the shift is shown to be uniquely ergodic with respect to the fixed-point algebra. In addition, for every m ≥ 1, the invariant states of the shift acting on the m-truncated t-free C*-algebra are shown to yield a m + 1-dimensional Choquet simplex, which collapses to a segment in the full case. Finally, the spectrum of the position operators on the m-truncated t-free Fock space is also determined.