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arXiv · 2208.00989

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

Vitonofrio Crismale·Simone Del Vecchio·Stefano Rossi
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Abstract

The ergodic properties of the shift on both full and $m$-truncated $t$-free $C^*$-algebras are analyzed. In particular, the shift is shown to be uniquely ergodic with respect to the fixed-point algebra. In addition, for every $m\geq 1$, 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.

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Vitonofrio Crismale, Simone Del Vecchio, Stefano Rossi. 2022-08-01. On truncated $t$-free Fock spaces: spectrum of position operators and shift-invariant states. https://arxiv.org/abs/2208.00989

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