Annals of Functional Analysis

Some trace monotonicity properties and applications

Jean-Michel Combes and Peter D. Hislop

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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

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

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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]

operator trace inequalities operator monotone functions Loewner’s Theorem random Schrodinger operators Wegner estimate


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.

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