## Taiwanese Journal of Mathematics

- Taiwanese J. Math.
- Volume 11, Number 2 (2007), 447-469.

### BOUNDED-LIPSCHITZ DISTANCES ON THE STATE SPACE OF A C*-ALGEBRA

#### Abstract

Metric noncommutative geometry, initiated by Alain Connes, has known some great recent developments under the impulsion of Rieffel and the introduction of the category of compact quantum metric spaces topologized thanks to the to quantum Rieffel-Gromov-Hausdorff distance. In this paper, we undertake the first step to generalize such results and constructions to locally compact quantum metric spaces. Our present work shows how to generalize the construction of the bounded-Lipschitz metric on the state space of a C*-algebra which need not be unital, such that the topology induced by this distance on the state space is the weak* topology. In doing so we obtain some results on a state space picture of the strict topology of a C*-algebra.

#### Article information

**Source**

Taiwanese J. Math., Volume 11, Number 2 (2007), 447-469.

**Dates**

First available in Project Euclid: 18 July 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.twjm/1500404701

**Digital Object Identifier**

doi:10.11650/twjm/1500404701

**Mathematical Reviews number (MathSciNet)**

MR2333358

**Zentralblatt MATH identifier**

1129.46063

**Subjects**

Primary: 46L89: Other "noncommutative" mathematics based on C-algebra theory [See also 58B32, 58B34, 58J22] 46L30: States

**Keywords**

quantum metric spaces strict topology Lip-norms state space

#### Citation

Latrémolière, Frédéric. BOUNDED-LIPSCHITZ DISTANCES ON THE STATE SPACE OF A C*-ALGEBRA. Taiwanese J. Math. 11 (2007), no. 2, 447--469. doi:10.11650/twjm/1500404701. https://projecteuclid.org/euclid.twjm/1500404701