HIGHER ORDER EXTENSION OF LOWNER'S THEORY: OPERATOR k-TONE FUNCTIONS

Affiliation auteursAffiliation ok
TitreHIGHER ORDER EXTENSION OF LOWNER'S THEORY: OPERATOR k-TONE FUNCTIONS
Type de publicationJournal Article
Year of Publication2014
AuteursFranz U, Hiai F, Ricard E
JournalTRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume366
PaginationPII S0002-9947(2014)05942-4
Date PublishedJUN
Type of ArticleArticle
ISSN0002-9947
Mots-clésabsolutely monotone function, completely monotone function, divided difference, matrix convex function, matrix k-tone function, matrix monotone function, operator convex function, operator k-tone function, Operator monotone function
Résumé

The new notion of operator/matrix k-tone functions is introduced, which is a higher order extension of operator/matrix monotone and convex functions. Differential properties of matrix k-tone functions are shown. Characterizations, properties, and examples of operator k-tone functions are presented. In particular, integral representations of operator k-tone functions are given, generalizing familiar representations of operator monotone and convex functions.
DOI10.1090/S0002-9947-2014-05942-4