English

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.

Keywords

Cite

@article{arxiv.0806.0782,
  title  = {Non-commutative Hardy inequalities},
  author = {Frank Hansen},
  journal= {arXiv preprint arXiv:0806.0782},
  year   = {2010}
}
R2 v1 2026-06-21T10:47:28.612Z