Refined Young inequalities with Specht’s ratio
Copyright policy )Refined Young inequalities with Specht’s ratio
In this paper, we show that the $��$-weighted arithmetic mean is greater than the product of the $��$-weighted geometric mean and Specht's ratio. As a corollary, we also show that the $��$-weighted geometric mean is greater than the product of the $��$-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.
A small mistake of calculation in page 4 was corrected. References were updated. 7 pages
- Nihon University Japan
- Nihon Bunka University Japan
Positive operator, operator mean, Young inequality, Operator mean and operator inequality, Positive linear operators and order-bounded operators, 15A45 and 47A63, operator inequality, Functional Analysis (math.FA), Mathematics - Functional Analysis, Specht's ratio, Specht’s ratio, FOS: Mathematics, Inequalities for sums, series and integrals, positive operator
Positive operator, operator mean, Young inequality, Operator mean and operator inequality, Positive linear operators and order-bounded operators, 15A45 and 47A63, operator inequality, Functional Analysis (math.FA), Mathematics - Functional Analysis, Specht's ratio, Specht’s ratio, FOS: Mathematics, Inequalities for sums, series and integrals, positive operator
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