Integration on locally compact noncommutative spaces

Understand

We present an ab initio approach to integration theory for nonunital spectral triples.

• This is done without reference to local units and in the full generality of semifinite noncommutative geometry.
• The main result is an equality between the Dixmier trace and generalised residue of the zeta function and heat kernel of suitable operators.
• We also examine definitions for integrable bounded elements of a spectral triple based on zeta function, heat kernel and Dixmier trace techniques.