Pure inductive limit state and Kolmogorov's property
| dc.creator | Mohari, Anilesh | |
| dc.date | 2007-04-16 | |
| dc.date.accessioned | 2026-07-07T07:56:43Z | |
| dc.date.available | 2026-07-07T07:56:43Z | |
| dc.description | Let $(\clb,λ_t,ψ)$ be a $C^*$-dynamical system where $(λ_t: t \in \IT_+)$ be a semigroup of injective endomorphism and $ψ$ be an $(λ_t)$ invariant state on the $C^*$ subalgebra $\clb$ and $\IT_+$ is either non-negative integers or real numbers. The central aim of this exposition is to find a useful criteria for the inductive limit state $\clb \raro^{λ_t} \clb$ canonically associated with $ψ$ to be pure. We achieve this by exploring the minimal weak forward and backward Markov processes associated with the Markov semigroup on the corner von-Neumann algebra of the support projection of the state $ψ$ to prove that Kolmogorov's property [Mo2] of the Markov semigroup is a sufficient condition for the inductive state to be pure. As an application of this criteria we find a sufficient condition for a translation invariant factor state on a one dimensional quantum spin chain to be pure. This criteria in a sense complements criteria obtained in [BJKW,Mo2] as we could go beyond lattice symmetric states. | |
| dc.identifier | https://arxiv.org/abs/0704.1987 | |
| dc.identifier | http://arxiv.org/abs/0704.1987 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127410 | |
| dc.subject | Operator Algebras | |
| dc.subject | Probability | |
| dc.subject | Inductive limit, Pure state, Kolmogorov's property, Markov shift | |
| dc.title | Pure inductive limit state and Kolmogorov's property | |
| dc.type | text |