Conjugate Dynamical Systems on C*-algebras

ar X iv : m at h / 04 02 30 9 v 1 [ m at h . O A ] 1 9 Fe b 20 04 Minimal Dynamical Systems and Approximate Conjugacy ∗

Several versions of approximate conjugacy for minimal dynamical systems are introduced. Relation between approximate conjugacy and corresponding crossed product C∗-algebras is discussed. For the Cantor minimal systems, a complete description is given for these relations via K-theory and C∗-algebras. For example, it is shown that two Cantor minimal systems are approximately τ -conjugate if and o...

Additive maps on C$^*$-algebras commuting with $|.|^k$ on normal elements

Let $mathcal {A} $ and $mathcal {B} $ be C$^*$-algebras. Assume that $mathcal {A}$ is of real rank zero and unital with unit $I$ and $k>0$ is a real number. It is shown that if $Phi:mathcal{A} tomathcal{B}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $Phi(|A|^k)=|Phi(A)|^k $ for all normal elements $Ainmathcal A$, $Phi(I)$ is a projection, and there exists a posit...

Semicrossed Products of Simple C*-algebras

Let (A, α) and (B, β) be C*-dynamical systems and assume that A is a separable simple C*-algebra and that α and β are ∗-automorphisms. Then the semicrossed products A×αZ and B ×β Z are isometrically isomorphic if and only if the dynamical systems (A, α) and (B, β) are outer conjugate.

On Strong Ergodic Properties of Quantum Dynamical Systems

Abstract. We show that the the shift on the reduced C∗–algebras of RD–groups, including the free group on infinitely many generators, and the amalgamated free product C∗–algebras, enjoys the very strong ergodic property of the convergence to the equilibrium. Namely, the free shift converges, pointwise in the weak topology, to the conditional expectation onto the fixed–point subalgebra. Provided...

Dynamical Systems on Hilbert C*-Modules