Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 7, Number 3 (2016), 394-401.
Some trace monotonicity properties and applications
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.
Ann. Funct. Anal. Volume 7, Number 3 (2016), 394-401.
Received: 3 August 2015
Accepted: 1 December 2015
First available in Project Euclid: 19 May 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]
Secondary: 47A60: Functional calculus 47B80: Random operators [See also 47H40, 60H25]
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