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.
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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. 361–375DOI 10.4171/JNCG/40