Local characterizations for the matrix monotonicity and convexity of fixed order
Functional Analysis
2017-03-03 v2
Abstract
We establish local characterizations of matrix monotonicity and convexity of fixed order by giving integral representations connecting the Loewner and Kraus matrices, previously known to characterize these properties, to respective Hankel matrices. Our results are new already in the general case of matrix convexity and our approach significantly simplifies the corresponding work on matrix monotonicity. We also obtain an extension of the original characterization for matrix convexity by Kraus, and tighten the relationship between monotonicity and convexity.
Keywords
Cite
@article{arxiv.1608.07516,
title = {Local characterizations for the matrix monotonicity and convexity of fixed order},
author = {Otte Heinävaara},
journal= {arXiv preprint arXiv:1608.07516},
year = {2017}
}
Comments
9 pages, no figures; a number of modifications made based on two referee reports; to appear in Proc. Amer. Math. Soc