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

Abstract

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.