一类渐近阿贝尔C*-代数的变分原理
The variational principle for a class of asymptotically abelian C*-algebras
AI总结：
该研究针对一类满足特定渐近交换条件的AF-系统，引入自同构在自伴算子处的压强概念，证明了对应变分原理，并明确了达到压强上确界的态的KMS性质及相关熵的结论。
摘要：
设(A,α)为一个C*-动力系统。我们引入自同构α在自伴算子H∈A处的压强P_α(H)的概念。随后我们研究满足以下条件的AF-系统（近似有限维系统）类：存在A的一个稠密的α-不变*-子代数\ud835\udc9c，使得对所有a,b∈\ud835\udc9c，二者生成的C*-代数是有限维的，且存在p=p(a,b)∈ℕ，当|j|≥p时[α^j(a),b]=0。对于这类系统，我们证明了变分原理，即P_α(H)是量h_ϕ(α)-ϕ(H)的上确界，其中h_ϕ(α)是α关于α-不变态ϕ的Connes-Narnhofer-Thirring动力熵。若H∈\ud835\udc9c且P_α(H)有限，我们证明达到该上确界的任意态都是相对于与H自然关联的单参数自同构群的KMS态。特别地，Voiculescu拓扑熵等于h_ϕ(α)的上确界，且任意具有有限最大熵的态都是迹态。
英文摘要：
Let (A,α) be a C*-dynamical system. We introduce the notion of pressure P_α(H) of the automorphism αat a self-adjoint operator H\in A. Then we consider the class of AF-systems satisfying the following condition: there exists a dense α-invariant *-subalgebra \A of A such that for all pairs a,b\in\A the C*-algebra they generate is finite dimensional, and there is p=p(a,b)\in\N such that [α^j(a),b]=0 for |j|\ge p. For systems in this class we prove the variational principle, i.e. show that P_α(H) is the supremum of the quantities h_ϕ(α)-ϕ(H), where h_ϕ(α) is the Connes-Narnhofer-Thirring dynamical entropy of αwith respect to the α-invariant state ϕ. If H\in\A, and P_α(H) is finite, we show that any state on which the supremum is attained is a KMS-state with respect to a one-parameter automorphism group naturally associated with H. In particular, Voiculescu's topological entropy is equal to the supremum of h_ϕ(α), and any state of finite maximal entropy is a trace.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
