English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let (A,\alpha) be a C*-dynamical system. We introduce the notion of pressureP_\alpha(H) of the automorphism \alpha at a self-adjoint operator H\in A. Thenwe consider the class of AF-systems satisfying the following condition: thereexists a dense \alpha-invariant *-subalgebra \A of A such that for all pairsa,b\in\A the C*-algebra they generate is finite dimensional, and there isp=p(a,b)\in\N such that [\alpha^j(a),b]=0 for |j|\ge p. For systems in thisclass we prove the variational principle, i.e. show that P_\alpha(H) is thesupremum of the quantities h_\phi(\alpha)-\phi(H), where h_\phi(\alpha) is theConnes-Narnhofer-Thirring dynamical entropy of \alpha with respect to the\alpha-invariant state \phi. If H\in\A, and P_\alpha(H) is finite, we show thatany state on which the supremum is attained is a KMS-state with respect to aone-parameter automorphism group naturally associated with H. In particular,Voiculescu's topological entropy is equal to the supremum of h_\phi(\alpha),and any state of finite maximal entropy is a trace.Comment: LaTeX2e, 20 page

The Variational Principle for a Class of Asymptotically Abelian C*-Algebras