## Annals of Functional Analysis

### Some trace monotonicity properties and applications

#### Abstract

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. The relation between these results and Löwner’s Theorem is discussed. We also apply these results to complete a proof of the Wegner estimate for continuum models of random Schrödinger operators as given in a 1994 paper by Combes and Hislop.

#### Article information

Source
Ann. Funct. Anal. Volume 7, Number 3 (2016), 394-401.

Dates
Accepted: 1 December 2015
First available in Project Euclid: 19 May 2016

https://projecteuclid.org/euclid.afa/1463684085

Digital Object Identifier
doi:10.1215/20088752-3605258

Mathematical Reviews number (MathSciNet)
MR3506611

Zentralblatt MATH identifier
1351.47013

#### Citation

Combes, Jean-Michel; Hislop, Peter D. Some trace monotonicity properties and applications. Ann. Funct. Anal. 7 (2016), no. 3, 394--401. doi:10.1215/20088752-3605258. https://projecteuclid.org/euclid.afa/1463684085

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