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On weights, traces and K-theory

Klaus Thomsen

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.

On weights, traces and K-theory

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.
Paper Structure (6 sections, 19 theorems, 104 equations)

This paper contains 6 sections, 19 theorems, 104 equations.

Table of Contents

  1. Introduction
  2. Weights
  3. Pairing weights with $K_{00}$
  4. Pairing traces with $K_0$
  5. Proof of Theorem \ref{['19-11-22d']}
  6. On lower semi-continuity of traces

Key Result

Lemma 2.1

Let $\psi$ be weight on $A$. The sets $\mathcal{M}_\psi$, $\mathcal{M}_\psi^+$ and $\mathcal{N}_\psi$ have the following properties.

Theorems & Definitions (36)

  • Lemma 2.1
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • Corollary 3.4
  • Lemma 3.5
  • proof
  • ...and 26 more