Some trace monotonicity properties and applications

Jean Michel Combes, Peter D. Hislop

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)394-401
Number of pages8
JournalAnnals of Functional Analysis
Volume7
Issue number3
DOIs
StatePublished - Aug 1 2016

Bibliographical note

Funding Information:
We thank the referees for useful comments. Some of this work was undertaken while Hislop was at the Université de Toulon, and he thanks that institution for its hospitality. Hislop's work was partially supported by National Science Foundation grant DMS-1103104.

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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