Some trace monotonicity properties and applications

J. -M. Combes (1, 2) , P. D. Hislop (3)

1 CPT - E8 Dynamique quantique et analyse spectrale
2 CPT - Centre de Physique Théorique - UMR 7332
3 University of Kentucky

We present some results on the monotonicity of some traces involving functions of self-adjoint operators with respect to the natural ordering of their associated quadratic forms. We also apply these results to complete a proof of the Wegner estimate for continuum models of random Schrödinger operators as given in \cite{co-hi1}.

Domaines: Analyse fonctionnelle [math.FA]; Physique mathématique [math-ph]

J. -M. Combes, P. D. Hislop. Some trace monotonicity properties and applications. Annals of Functional Analysis, 2016, 7 (3), pp.394-401. ⟨10.1215/20088752-3605258⟩. ⟨hal-01265676⟩