Some trace monotonicity properties and applications

Jean Michel Combes; Peter D. Hislop

doi:10.1215/20088752-3605258

Some trace monotonicity properties and applications

Jean Michel Combes, Peter D. Hislop

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	394-401
Number of pages	8
Journal	Annals of Functional Analysis
Volume	7
Issue number	3
DOIs	https://doi.org/10.1215/20088752-3605258
State	Published - Aug 1 2016

Bibliographical note

Publisher Copyright:
© 2016 by the Tusi Mathematical Research Group.

Keywords

Loewner's theorem
Operator monotone functions
Operator trace inequalities
Random schrodinger operators
Wegner estimate

ASJC Scopus subject areas

Analysis
Anatomy
Algebra and Number Theory

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10.1215/20088752-3605258

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AB - 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.

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KW - Operator trace inequalities

KW - Random schrodinger operators

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Some trace monotonicity properties and applications

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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