Higher order extension of L\"owner's theory: Operator $k$-tone functions
Functional Analysis
2014-05-19 v4 Operator Algebras
Abstract
The new notion of operator/matrix -tone functions is introduced, which is a higher order extension of operator/matrix monotone and convex functions. Differential properties of matrix -tone functions are shown. Characterizations, properties, and examples of operator -tone functions are presented. In particular, integral representations of operator -tone functions are given, generalizing familiar representations of operator monotone and convex functions.
Keywords
Cite
@article{arxiv.1105.3881,
title = {Higher order extension of L\"owner's theory: Operator $k$-tone functions},
author = {Uwe Franz and Fumio Hiai and Éric Ricard},
journal= {arXiv preprint arXiv:1105.3881},
year = {2014}
}
Comments
final version, 33 pages