Modulation Spaces as a Smooth Structure in Noncommutative Geometry

Abstract

We demonstrate that a class of modulation spaces are examples of a smooth structure on the noncommutative 2-torus in the sense of recent developments in KK-theory. In addition, we prove that this class of modulation spaces can be represented as corners in operator linking algebras.

Largely revised version. We removed the material on operator spaces and we extended our results to locally compact abelian groups