Approximately Finite $C^*$-Algebras and Partial Automorphisms.

Approximately Finite Algebras

APPROXIMATELY INNER sigma-DYNAMICS ON C* ALGEBRAS

On the C*-envelope of approximately finite-dimensional operator algebras

The C*-envelope of the limit algebra (or limit space) of a contrac-tive regular system of digraph algebras (or digraph spaces) is shown to be an approximately finite C*-algebra and the direct system for the C*-envelope is determined explicitly.

Time Automorphisms on C ∗ - Algebras

Applications of fractional time derivatives in physics and engineering require the existence of nontranslational time automorphisms on the appropriate algebra of observables. The existence of time automorphisms on commutative and noncommutative C∗-algebras for interacting many-body systems is investigated in this article. A mathematical framework is given to discuss local stationarity in time a...

Local Characterisation of Approximately Finite Operator Algebras

We show that the family of nest algebras with r non-zero nest projections is stable, in the sense that an approximate containment of one such algebra within another is close to an exact containment. We use this result to give a local characterisation of limits formed from this family. We then consider quite general regular limit algebras and characterise these algebras using a local condition w...