Complete Positivity of Rieffel's Deformation Quantization by Actions of $\mathbb{R}^d$

Kaschek, Daniel; Neumaier, Nikolai; Waldmann, Stefan

Complete Positivity of Rieffel's Deformation Quantization by Actions of $\mathbb{R}^d$

Authors

Kaschek, Daniel

Neumaier, Nikolai

Waldmann, Stefan

Description

In this paper we consider C*-algebraic deformations a 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.
17 pages. New (more precise) title and other minor changes. Final version