Note on L\"owner's theorem on matrix monotone functions in several commuting variables of Agler, McCarthy and Young
Functional Analysis
2014-09-10 v1 Complex Variables
Abstract
In this brief note, we show that the hypotheses of L\"owner's theorem on matrix monotonicity in several commuting variables as proved by Agler, McCarthy and Young can be significantly relaxed. Specifically, we extend their theorem from continuously differentiable locally matrix monotone functions to arbitrary locally matrix monotone functions using mollification techniques.
Keywords
Cite
@article{arxiv.1409.2605,
title = {Note on L\"owner's theorem on matrix monotone functions in several commuting variables of Agler, McCarthy and Young},
author = {J. E. Pascoe},
journal= {arXiv preprint arXiv:1409.2605},
year = {2014}
}