Refined Young inequalities with Specht's ratio

Details Refined Young inequalities with Specht's ratio Refined Young inequalities with Specht's ratio

2010-04-05

arxiv.org/abs/1004.0581v3

Mathematics

Functional Analysis

A small mistake of calculation in page 4 was corrected. References were updated. 7 pages

Scientific paper

In this paper, we show that the $\nu$-weighted arithmetic mean is greater than the product of the $\nu$-weighted geometric mean and Specht's ratio. As a corollary, we also show that the $\nu$-weighted geometric mean is greater than the product of the $\nu$-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.

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