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  Volume 4, Issue 2, Article 40
Reverse Inequalities on Chaotically Geometric Mean via Specht Ratio, II

    Authors: Masatoshi Fujii, Jadranka Micic, Josip E. Pecaric, Yuki Seo,  
    Keywords: Operator concavity, Power mean, Arithmetic mean, Geometric mean.  
    Date Received: 24/01/03  
    Date Accepted: 05/03/03  
    Subject Codes:

47A30, 47A63.

    Editors: Saburou Saitoh,  

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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