Dixmier trace and the DOS of magnetic operators

The main goal of this work is to provide two new formulas for the computation of the trace per unit volume, and consequently the integrated density of states (IDOS), for magnetic operators. These formulas also allow the use of the Dixmier trace in the spectral analysis of magnetic operators. The second of these formulas, named energy shell formula , allows us to approximate the IDOS by a finite sum of averaged expectation values of the spectral projections.