Complete positivity of Rieffel’s deformation quantization by actions of ℝ<sup><var>d</var></sup>
Daniel Kaschek
University of Freiburg, GermanyNikolai Neumaier
University of Freiburg, GermanyStefan Waldmann
University of Freiburg, Germany

Abstract
In this paper we consider C*-algebraic deformations by actions of ℝd à la Rieffel and show that every state of the undeformed algebra can be deformed into a state of the deformed algebra in the sense of a continuous field of states. The construction is explicit and involves a convolution operator with a particular Gauß function.
Cite this article
Daniel Kaschek, Nikolai Neumaier, Stefan Waldmann, Complete positivity of Rieffel’s deformation quantization by actions of ℝ<sup><var>d</var></sup>. J. Noncommut. Geom. 3 (2009), no. 3, pp. 361–375
DOI 10.4171/JNCG/40