## Tokyo Journal of Mathematics

### Approximately Inner $*$-Derivations of Irrational Rotation $C^*$-Algebras

Kazunori KODAKA

#### Abstract

Let $\theta$ be an irrational number and $A_\theta$ be the corresponding irrational rotation $C^*$-algebra. For any $k\in N\cup\{\infty\}$ let $A_\theta^k$ be the dense $*$-subalgebra of $k$-times continuously differentiable elements in $A_\theta$ with respect to the canonical action of the two dimensional torus and let $A_\theta^0=A_\theta$. In the present paper we will show that there is an approximately inner $*$-derivation of $A_\theta^\infty$ to $A_\theta^\infty$ which is not inner if and only if $\theta$ is a non-generic irrational number.

#### Article information

Source
Tokyo J. Math., Volume 13, Number 1 (1990), 207-219.

Dates
First available in Project Euclid: 1 April 2010

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1270133015

Digital Object Identifier
doi:10.3836/tjm/1270133015

Mathematical Reviews number (MathSciNet)
MR1059025

Zentralblatt MATH identifier
0723.46045

#### Citation

KODAKA, Kazunori. Approximately Inner $*$-Derivations of Irrational Rotation $C^*$-Algebras. Tokyo J. Math. 13 (1990), no. 1, 207--219. doi:10.3836/tjm/1270133015. https://projecteuclid.org/euclid.tjm/1270133015