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

Producción científica: Article › revisión exhaustiva

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	394-401
Número de páginas	8
Publicación	Annals of Functional Analysis
Volumen	7
N.º	3
DOI	https://doi.org/10.1215/20088752-3605258
Estado	Published - ago 1 2016

Nota bibliográfica

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

Financiación

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.

Financiadores	Número del financiador
Université de Toulon
National Science Foundation Arctic Social Science Program	DMS-1103104

ASJC Scopus subject areas

Analysis
Anatomy
Algebra and Number Theory

Acceder al documento

10.1215/20088752-3605258

Otros archivos y enlaces

Citar esto

@article{5e6c8882dd8941d88dd359e04787bc2d,

title = "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 L{\"o}wner's Theorem is discussed. We also apply these results to complete a proof of the Wegner estimate for continuum models of random Schr{\"o}dinger operators as given in a 1994 paper by Combes and Hislop.",

keywords = "Loewner's theorem, Operator monotone functions, Operator trace inequalities, Random schrodinger operators, Wegner estimate",

author = "Combes, \{Jean Michel\} and Hislop, \{Peter D.\}",

note = "Publisher Copyright: {\textcopyright} 2016 by the Tusi Mathematical Research Group.",

year = "2016",

month = aug,

day = "1",

doi = "10.1215/20088752-3605258",

language = "English",

volume = "7",

pages = "394--401",

number = "3",

}

TY - JOUR

T1 - Some trace monotonicity properties and applications

AU - Combes, Jean Michel

AU - Hislop, Peter D.

PY - 2016/8/1

Y1 - 2016/8/1

N2 - 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.

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.

KW - Loewner's theorem

KW - Operator monotone functions

KW - Operator trace inequalities

KW - Random schrodinger operators

KW - Wegner estimate

UR - https://www.scopus.com/pages/publications/84974663313

UR - https://www.scopus.com/pages/publications/84974663313#tab=citedBy

U2 - 10.1215/20088752-3605258

DO - 10.1215/20088752-3605258

M3 - Article

AN - SCOPUS:84974663313

SN - 2008-8752

VL - 7

SP - 394

EP - 401

JO - Annals of Functional Analysis

JF - Annals of Functional Analysis

IS - 3

ER -

Some trace monotonicity properties and applications

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

Acceder al documento

Otros archivos y enlaces

Huella

Citar esto