Noncommutative topological dynamics and compact actions on C∗-algebras

Compact actions commuting with ergodic actions and applications to crossed products

“…By formula (8) in §2 a\ ± (0). But A^(n) can be defined for every finite dimensional representation n £ Yl(K).…”

“…Conversely, if [a¡j] £ A2CJ1), then by denoting a = J2 aa > a standard calculation using the orthogonality relations shows that Pnjj(a) = a¡¡ for all 1 < i, j < dim n so that we have the following equality (8) {[PßlJ(a)]\a£A} = Aß(n).…”

“…Namely a is called topologically transitive if for every two nonzero, globally G-invariant, hereditary C*-subalgebras Bx, Bi of A , their product is nonzero. As an application of our techniques and notions we proved [8] some duality results for compact abelian actions commuting with ergodic actions. Subsequently in [2] a seemingly stronger notion of ergodicity called strong topological transitivity was considered.…”

“…In [8] the notion of topological transitivity was introduced. Namely a is called topologically transitive if for every two nonzero, globally G-invariant, hereditary C*-subalgebras Bx, Bi of A , their product is nonzero.…”

Topological transitivity of compact actions on 𝐶*-algebras

“…We shall denote by Aa the fixed point C*-subalgebra of (A, G, a) and by Ha(A) the set of all nonzero ainvariant hereditary C*-subalgebras of A. In [5], the authors define the Cdynamical system (A, G, a) as …”