English

On refined Young inequalities and reverse inequalities

Functional Analysis 2011-04-26 v4

Abstract

In this paper, we show refined Young inequalities for two positive operators. Our results refine the ordering relations among the arithmetic mean, the geometric mean and the harmonic mean for two positive operators. In addition, we give two different reverse inequalities for the refined Young inequality for two positive operators.

Keywords

Cite

@article{arxiv.1001.0535,
  title  = {On refined Young inequalities and reverse inequalities},
  author = {Shigeru Furuichi},
  journal= {arXiv preprint arXiv:1001.0535},
  year   = {2011}
}

Comments

The arised problem in Remark 4.2 in the previous manuscript was partially solved by finding a counter-example. Thus 5 lines from the below in page 8 were deleted

R2 v1 2026-06-21T14:30:44.186Z