## Journal of the Mathematical Society of Japan

### Hulls and kernels from topological dynamical systems and their applications to homeomorphism $C^{*}$ -algebras

Jun TOMIYAMA

#### Abstract

For a topological dynamical system $\Sigma$$=(X,\sigma)$ where $\sigma$ is a homeomorphism in an arbitrary compact Hausdorff space $X$, we consider the noncommutative hulls and kernels with respect to the action $\sigma$ in the associated $C*-$ algebra $A(\Sigma)$. We show that several ideals important for the structure of $A(\Sigma)$ have the form of such kernels and give topological characterizations of their hulls from the behavior of orbits in the dynamical system.

#### Article information

Source
J. Math. Soc. Japan, Volume 56, Number 2 (2004), 349-364.

Dates
First available in Project Euclid: 3 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191418634

Digital Object Identifier
doi:10.2969/jmsj/1191418634

Mathematical Reviews number (MathSciNet)
MR2048463

Zentralblatt MATH identifier
1064.46054

#### Citation

TOMIYAMA, Jun. Hulls and kernels from topological dynamical systems and their applications to homeomorphism $C^{*}$ -algebras. J. Math. Soc. Japan 56 (2004), no. 2, 349--364. doi:10.2969/jmsj/1191418634. https://projecteuclid.org/euclid.jmsj/1191418634