Non-commutative Hardy inequalities
Operator Algebras
2010-01-13 v2 Mathematical Physics
math.MP
Abstract
We extend Hardy's inequality from sequences of non-negative numbers to sequences of positive semi-definite operators if the parameter p satisfies 1<p<=2, and to operators under a trace for arbitrary p>1. Applications to trace functions are given. We introduce the tracial geometric mean and generalize Carleman's inequality. Key words and phrases: Hardy's inequality, positive operator, trace function, geometric mean, Carleman's inequality.
Cite
@article{arxiv.0806.0782,
title = {Non-commutative Hardy inequalities},
author = {Frank Hansen},
journal= {arXiv preprint arXiv:0806.0782},
year = {2010}
}