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Volume 4, Issue 2, Article 40 |
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Reverse Inequalities on Chaotically Geometric Mean via Specht Ratio, II
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Authors: |
Masatoshi Fujii, Jadranka Micic, Josip E. Pecaric, Yuki Seo, |
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Keywords:
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Operator concavity, Power mean, Arithmetic mean, Geometric mean. |
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Date Received:
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24/01/03 |
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Date Accepted:
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05/03/03 |
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Subject Codes: |
47A30, 47A63.
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Editors: |
Saburou Saitoh, |
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Abstract: |
In 1967, as a converse of the arithmetic-geometric mean inequality, Mond and Shisha gave an estimate of the difference between the arithmtic mean and the geometric one, which we call it the Mond-Shisha difference. As an application of Mond-Pecaric method, we show some order relations between the power means of positive operators on a Hilbert space. Among others, we show that the upper bound of the difference between the arithmetic mean and the chaotically geometric one of positive operators coincides with the Mond-Shisha difference.
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