On weights, traces and K-theory

TL;DR

This paper extends the pairing between the K0 group of a C*-algebra and its traces to a broader pairing with weights, removing previous semi-continuity constraints and enhancing the theoretical framework.

Contribution

It introduces a method to extend the pairing from traces to weights for the K0 group of C*-algebras, eliminating the semi-continuity assumption.

Findings

Pairing of K0 with weights extends previous trace pairing.

The extension removes the need for semi-continuity assumptions.

Provides a more general theoretical framework for K-theory and weights.

Abstract

It is shown that the pairing of the K00 group of a C*-algebra with the densely defined traces of the algebra can be extended to a pairing with the densely defined weights. For traces the pairing can be extended to the K0 group without the semi-continuity assumption occurring in the work of Connes and Elliott.