Modulation Spaces as a Smooth Structure in Noncommutative Geometry

TL;DR

This paper shows that certain modulation spaces serve as a smooth structure on the noncommutative 2-torus, linking functional analysis with noncommutative geometry through KK-theory and operator algebras.

Contribution

It introduces modulation spaces as a new smooth structure in noncommutative geometry and connects them to operator linking algebras.

Findings

Modulation spaces form a smooth structure on the noncommutative 2-torus.

These spaces can be represented as corners in operator linking algebras.

The work bridges modulation spaces with KK-theory 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.