## Journal of the Mathematical Society of Japan

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

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

#### 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 $C\text{*}-$ algebra $A\left(\Sigma \right)$. We show that several ideals important for the structure of $A\left(\Sigma \right)$ 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

**Subjects**

Primary: 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20] 37A55: Relations with the theory of C-algebras [See mainly 46L55] 54H15: Transformation groups and semigroups [See also 20M20, 22-XX, 57Sxx]

**Keywords**

Homeomorphism noncommutative hull-kernel crossed product recurrent point periodic point

#### 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