English

Operator inequalities among arithmetic mean, geometric mean and harmonic mean

Functional Analysis 2014-10-21 v1

Abstract

We give an upper bound for the weighted geometric mean using the weighted arithmetic mean and the weighted harmonic mean. We also give a lower bound for the weighted geometric mean. These inequalities are proven for two invertible positive operators.

Keywords

Cite

@article{arxiv.1410.4905,
  title  = {Operator inequalities among arithmetic mean, geometric mean and harmonic mean},
  author = {Shigeru Furuichi},
  journal= {arXiv preprint arXiv:1410.4905},
  year   = {2014}
}

Comments

4 pages

R2 v1 2026-06-22T06:27:58.927Z