JournalsjncgVol. 3 , No. 3DOI 10.4171/jncg/40

Complete positivity of Rieffel’s deformation quantization by actions of ℝ<sup><var>d</var></sup>

  • Daniel Kaschek

    University of Freiburg, Germany
  • Nikolai Neumaier

    University of Freiburg, Germany
  • Stefan Waldmann

    University of Freiburg, Germany
Complete positivity of Rieffel’s deformation quantization by actions of ℝ<sup><var>d</var></sup> cover

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.