2010/04/05 by Shigeru Furuichi, Furuichi, Shigeru
Mathematics · #15A45 and 47A63 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Mathematics and Applications #math.FA #msc:15A45 #msc:47A63
paper · pdf · doi:10.48550/arxiv.1004.0581
A small mistake of calculation in page 4 was corrected. References were updated. 7 pages
openalex publication_date 2010/04/05 · arxiv created 2011/03/09 · arxiv updated 2011/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we show that the ν-weighted arithmetic mean is greater than the product of the ν-weighted geometric mean and Specht's ratio. As a corollary, we also show that the ν-weighted geometric mean is greater than the product of the ν-weighted harmonic mean and Specht's ratio. These results give the improvements for the classical Young inequalities, since Specht's ratio is generally greater than 1. In addition, we give an operator inequality for positive operators, applying our refined Young inequality.