Taiwanese Journal of Mathematics

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

Frédéric Latrémolière

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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


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